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WHERE IS SCIENCE GOING?

Books by Max Planck

WHERE IS SCIENCE GOING?
THE UNIVERSE IN THE LIGHT OF
MODERN PHYSICS

WHERE IS
SGIENGE GOING?

BY MAX PLANCK

PROFESSOR OF THEORETICAL PHYSICS AT
THE UNIVERSITY OF BERLIN

*

PROLOGUE BY ALBERT EINSTEIN
TRANSLATION AND BIOGRAPHICAL NOTE
BY JAMES MURPHY

NEW YORK
W. W. NORTON & COMPANY, INC.
PUBLISHERS

Copyright, 1932
W. W. NORTON & COMPANY, INC
70 Fifth Avenue, New York

First Edition

PRINTED IN THE UNITED STATES OF AMERICA
FOR THE PURLISHERS D Y THE VAN REES PRESS

CONTENTS

PROLOGUE BY ALBERT EINSTEIN 7

INTRODUCTION BY JAMES MURPHY 13

I. FIFTY YEARS OF SCIENCE 41

II. IS THE EXTERNAL WORLD REAL? 64

III. THE SCIENTIST'S PICTURE OF THE PHYSICAL
UNIVERSE 84

IV. CAUSATION AND FREE WILL: THE PROBLEM
STATED 107

V. CAUSATION AND FREE WILL: THE ANSWER

OF SCIENCE i4I

VI. FROM THE RELATIVE TO THE ABSOLUTE,

Discussion of atomic weights, conceft of energy;
difference between reversible and irreversible froc esses 170

EPILOGUE: A SOCRATIC DIALOGUE. PLANCK-
EINSTEIN— MURPHY 201

PROLOGUE
BY ALBERT EINSTEIN

MANY kinds of men devote themselves to Sci-
ence, and not all for the sake of Science herself.
There are some who come into her temple because it
offers them the opportunity to display their particular
talents. To this class of men science is a kind of sport
in the practice of which they exult, just as an athlete
exults in the exercise of his muscular prowess. There
is another class of men who come into the temple to
make an offering of their brain pulp in the hope of se-
curing a profitable return. These men are scientists
only by the chance of some circumstance which offered
itself when making a choice of career. If the attending
circumstance had been different they might have be-
come politicians or captains of business. Should an angel
of God descend and drive from the Temple of Science
all those who belong to the categories I have men-
tioned, I fear the temple would be nearly emptied. But
a few worshipers would still remain — some from
former times and some from ours. To these latter be-
longs our Planck. And that is why we love him.

I am quite aware that this clearance would mean the
driving away of many worthy people who have built

7

8 WHERE IS SCIENCE GOING?

a great portion, and even perhaps the greatest portion,
of the Temple of Science. But at the same time it is
clear that if the men who have devoted themselves to
science consisted only of the two categories I have men-
tioned, the edifice could never have grown to its pres-
ent proud dimensions, no more than a forest could
grow if it consisted only of creepers.

But let us forget them. Non ragionam di lor. And
let us fix our gaze on those who have found favor with
the angel. For the most part they are strange, taciturn
and lonely fellows. And, in spite of this mutual re-
semblance, they are far less like one another than those
whom our hypothetical angel has expelled.

What has led them to devote their lives to the pur-
suit of science? That question is difficult to answer and
could never be answered in a simple categorical way.
Personally I am inclined to agree with Schopenhauer
in thinking that one of the strongest motives that lead
people to give their lives to art and science is the urge
to flee from everyday life, with its drab and deadly
dullness, and thus to unshackle the chains of one's own
transient desires, which supplant one another in an
interminable succession so long as the mind is fixed on
the horizon of daily environment.

But to this negative motive a positive one must be
added. Human nature always has tried to form for
itself a simple and synoptic image of the surrounding
world. In doing this it tries to construct a picture which
will give some sort of tangible expression to what the
human mind sees in nature. That is what the poet does,

PROLOGUE 9

and the painter, and the speculative philosopher and
the natural philosopher, each in his own way. Within
this picture he places the center of gravity of his own
soul, so that he will find in it that rest and equilibrium
which he cannot find within the narrow circle of his
restless personal reactions to everyday life.

Among the various pictures of the world which are
formed by the artist and the philosopher and the poet,
what place does the world-picture of the theoretical
physicist occupy? Its chief quality must be a scrupulous
correctness and internal logical coherence, which only
the language of mathematics can express. On the other
hand, the physicist has to be severe and self-denying
in regard to the material he uses. He has to be content
with reproducing the most simple processes that are
open to our sensory experience, because the more com-
plex processes cannot be represented by the human
mind with the subtle exactness and logical sequence
which are indispensable for the theoretical physicist.

Even at the expense of completeness, we have to
secure purity, clarity and accurate correspondence be-
tween the representation and the thing represented.
When one realizes how small a part of nature can thus
be comprehended and expressed in an exact formula-
tion, while all that is subtle and complex has to be
excluded, it is only natural to ask, what sort of attrac-
tion this work can have? Does the result of such self-
denying selection deserve the high-sounding name of
World-Picture?

I think it does; because the most general laws on

io WHERE IS SCIENCE GOING?

which the thought-structure of theoretical physics is
built have to be taken into consideration in studying
even the simplest events in nature. If they were fully
known one ought to be able to deduce from them by
means of purely abstract reasoning the theory of every
process of nature, including that of life itself. I mean
theoretically , because in practice such a process of de-
duction is entirely beyond the capacity of human rea-
soning. Therefore the fact that in science we have to
be content with an incomplete picture of the physical
universe is not due to the nature of the universe itself
but rather to us.

Thus the supreme task of the physicist is the dis-
covery of the most general elementary laws from
which the world-picture can be deduced logically. But
there is no logical way to the discovery of these ele-
mental laws. There is only the way of intuition, which
is helped by a feeling for the order lying behind the
appearance and this Einfuehlung is developed by ex-
perience. Can one therefore say that any system of
physics might be equally valid and possible? Theo-
retically there is nothing illogical in that idea. But the
history of scientific development has shown that of all
thinkable theoretical structures a single one has at each
stage of advance proved superior to all the others.

It is obvious to every experienced researcher that
the theoretical system of physics is dependent upon and
controlled by the world of sense-perception, though
there is no logical way whereby we can proceed from
sensory perception to the principles that underlie the

PROLOGUE

ii

theoretical structure. Moreover, the conceptual syn-
thesis which is a transcript of the empirical world may
be reduced to a few fundamental laws on which the
whole synthesis is logically built. In every important
advance the physicist finds that the fundamental
laws are simplified more and more as experimental
research advances. He is astonished to notice how
sublime order emerges from what appeared to be
chaos. And this cannot be traced back to the workings
of his own mind but is due to a quality that is inherent
in the world of perception. Leibniz well expressed this
quality by calling it a preestablished harmony.

Physicists sometimes reproach the philosophers who
busy themselves with theories of knowledge, claim-
ing that the latter do not appreciate this fact fully.
And I think that this was at the basis of the con-
troversy waged a few years ago between Ernst Mach
and Max Planck. The latter probably felt that Mach
did not fully appreciate the physicist's longing for
perception of this preestablished harmony. This long-
ing has been the inexhaustible source of that patience
and persistence with which we have seen Planck de-
voting himself to the most ordinary questions arising
in connection with physical science, when he might
have been tempted into other ways which led to more
attractive results.

I have often heard that his colleagues are in the
habit of tracing this attitude to his extraordinary per-
sonal gifts of energy and discipline. I believe they
are wrong. The state of mind which furnishes the

12 WHERE IS SCIENCE GOING?

driving power here resembles that of the devotee or
the lover. The long-sustained effort is not inspired by
any set plan or purpose. Its inspiration arises from a
hunger of the soul.

I am sure Max Planck would laugh at my childish
way of poking around with the lantern of Diogenes.
Well! why should I tell of his greatness? It needs no
paltry confirmation of mine. His work has given one
of the most powerful of all impulses to the progress
of science. His ideas will be effective as long as physi-
cal science lasts. And I hope that the example which
his personal life affords will not be less effective with
later generations of scientists.

INTRODUCTION

MAX PLANCK
A BIOGRAPHICAL SKETCH
BY JAMES MURPHY

ONE day in June 1932 I paid a visit to Albert
Einstein at his summer home in Caputh, some
fifteen miles west of Berlin. We had a long-drawn-out
tea together on a multitude of topics, from the chances
of the various political parties at the coming election
to the chances of somebody finally discovering a simple
formula for the unification of all physical laws. The
house is pitched high on a terraced slope and overlooks
a beautiful lake. Level with the upper story there is
a veranda which is like the spacious platform of an
observatory station. And there is a telescope with which
Einstein amuses himself by gazing on the stars. When
dusk came on, and the blazing sunlight that had been
beating on the lake all day was turning to a mellow
glow, we went for a stroll on the veranda to watch
the sunset and while away the time until the evening
meal would be ready. Within doors the political crisis
had been the central topic of conversation $ but here,

13

14 WHERE IS SCIENCE GOING?

amid the natural harmony of lake and forest and
sinking sun, a higher theme made its appeal.

The name of Max Planck came into our talk, and
the various philosophical problems which quantum
physics have given rise to. To my more sweeping
generalities Einstein would most invariably reply
"Nein, das kann man nicht sagen." But when I put
forward something more qualified he would reflect
for a while and say, "Ja, das können Sie sagen" We
were agreed, I think, that though the relativity theory
has captured the imagination of the world, the quantum
theory has been a more fundamental force in bringing
about the modern revolution in scientific thought.

While we were on this point I asked Einstein to
write me an introduction for a book of essays by Planck,
to be published in English. Einstein shied at the sug-
gestion. He said that it would be presumptuous on
his part to introduce Max Planck to the public 5 for the
discoverer of the quantum theory did not need the
reflected light of any lesser luminary to show him
off. That was Einstein's attitude towards Planck,
expressed with genuine and naive emphasis.

I explained that the book in question would be for
the general public and that, though the name of «Planck
is a household word in Germany and with scientists
all the world over, he is not so popular in English-
speaking countries as the founder of the relativity
theory. Einstein did not consider this a very regrettable
circumstance. He would have been pleased if the truth
were the other way round. But my point was that it

INTRODUCTION 15

is a good rule of logic to define the less known through
the better known, no matter what the objective merits
of the one or the other may be. He submitted to
the force of this argument and agreed to a short intro-
duction but insisted that it must be short, for anything
long would be pretentious.

The present chapter is not an enlargement on
Einstein's introduction. It is meant rather to be a
biographical sketch of a purely objective kind. My
first task here is to indicate the place which the author
of the following chapters holds in the modern develop-
ment of physical science. Then I shall endeavor to
describe for the reader, as simply and as vividly as
I can, the personality of Max Planck — his scientific
career, his attitude towards the function of theoretical
physics as an intellectual force in the modern everyday
world, his philosophy of life, his contemporary activi-
ties as a citizen and man of learning, and finally, his
place and prestige among his own people.

The first part of this task will be best discharged if
I leave it to a few leaders amongst Planck's colleagues
to define the place he holds in the general picture of
modern scientific progress.

What significance has the name of Max Planck in
the history of Physics? The answer to that question
can be indicated by pointing to the position which a
portrait of Max Planck would occupy in a pictorial
representation illustrating the development of science.
At the end of a long gallery there is a turning and a
wide space or angle of the wall. On that space the

i6 WHERE IS SCIENCE GOING?

portrait of Max Planck hangs, with one hand taking
grateful leave of the classical past and the other
pointing to a new corridor where the paint is hardly
yet dry on the portraits that hang there — Einstein,
Niels Bohr, Rutherford, Dirac, Eddington, Jeans,
Millikan, Wilson, Compton, Heisenberg, Schroed-
inger, etc., etc. Sir James Jeans, in his popular little
book The Mysterious Universe, describes the position
thus: 1

"At the end of the nineteenth century it first became
possible to study the behavior of single molecules,
atoms and electrons. The century had lasted just long
enough for science to discover that certain phenomena,
radiation and gravitation in particular, defied all at-
tempts at a purely mechanical explanation. While
philosophers were still debating whether a machine
could be constructed to reproduce the thoughts of
Newton, the emotions of Bach or the inspiration of
Michelangelo, the average men of science were rapidly
becoming convinced that no machine could be con-
structed to reproduce the light of a candle or the fall
of an apple. Then, in the closing months of the cen-
tury, Professor Max Planck of Berlin brought forward
a tentative explanation of certain phenomena of radia-
tion which had so far completely defied interpretation.
Not only was his explanation non-mechanical in its
nature j it seemed impossible to connect it up with any
mechanical line of thought. Largely for this reason,
it was criticized, attacked and even ridiculed. But it

1 The Mysterious Universe, 1932 edition, pp. 16 and 17.

INTRODUCTION 17

proved brilliantly successful, and ultimately devel-
oped into the modern 'quantum theory,' which forms
one of the dominating principles of modern physics.
Also, although this was not apparent at the time, it
marked the end of the mechanical age in science, and
the opening of a new era."

Another British scientist, Lord Rutherford, gives the
following estimate of his German colleague:

"The name of Planck is a household word among
the scientific men of all countries and all unite in their
admiration for his great and enduring contributions to
Physical Science.

"It is difficult to realize to-day, when the quantum
theory is successfully applied in so many fields of
science, how strange and almost fantastic this new con-
ception of radiation appeared to many scientific men
thirty years ago. It was difficult at first to obtain
any convincing proof of the correctness of the theory
and the deductions that followed from it. In this con-
nection I may refer to experiments made by Professor
Geiger and myself in 1908. On my side, the agree-
ment with Planck's deduction of e (e is the elementary
electric charge and the value is expressed in electro-
static units) made me an early adherent to the gen-
eral idea of a quantum of action. I was in consequence
able to view witK equanimity and even to encourage
Professor Bohr's bold application of the quantum
theory propounded by Planck." 1

The significance of Planck's achievement is thus

1 Die Naturwissenschaften, Vol. 26, p. 483.

18 WHERE IS SCIENCE GOING?

described by Niels Bohr, the famous Danish physicist:
"Scarcely any other discovery in the history of
science has produced such extraordinary results within
the short span of our generation as those which have
directly arisen from Max Planck's discovery of the
elementary quantum of action. This discovery has been
prolific, to a constantly increasing degree of progres-
sion, in furnishing means for the interpretation and
harmonizing of results obtained from the study of
atomic phenomena, which is a study that has made
marvelous progress within the past thirty years. But
the quantum theory has done something more. It has
brought about a radical revolution in the scientific in-
terpretation of natural phenomena. This revolution is
a direct development of theories and concepts which
originated from the pioneering work done by Max
Planck in studying cavity radiation. Within the past
thirty years these theories and concepts have grown
and expanded into that scientific elaboration which is
called quantum physics. The picture of the universe
formed on the lines of quantum physics must be looked
upon as a generalization that is independent of classical
physics, with which it compares favorably for its beauty
of conception and the inner harmony of its logic.

"I should like emphatically to call attention to the
consequences of this new knowledge. It has shattered
the foundations of our ideas not only in the realm of
classical science but also in our everyday ways of
thinking. It is to this emancipation from inherited
traditions of thought that we owe the wonderful

INTRODUCTION 19

progress which has been made in our knowledge of
natural phenomena during the past generation. That
progress has gone beyond even the highest hopes to
which it gave rise a few years ago. And the present
state of physical science can probably be indicated best
by saying that nearly all the lines of thought which
have led to fruitful results in experimental research
have naturally blended together into a common har-
mony without thereby losing their individual fertility.
For having placed in our hands the means of bring-
ing about these results the discoverer of the quantum
theory deserves the unqualified gratitude of his
colleagues!" 1

One name more will be sufficient to add to this
distinguished list. It is that of Professor Heisenberg,
the Leipzig physicist, who is the founder of the now
popular Theory of Indeterminacy. Heisenberg writes
as follows:

"In 1900 Max Planck published the following
statement: Radiant heat is not a continuous flow and
indefinitely divisible. It must be defined as a discon-
tinuous mass made uf of units all of which are similar
to one another.

"At that time he could scarcely have foreseen that
within a span of less than thirty years this theory,
which flatly contradicted the principles of physics
hitherto known, would have developed into a doctrine
of atomic structure which, for its scientific comprehen-

1 Die 'Naturwissenschaften, Vol. 26, p. 490.

20 WHERE IS SCIENCE GOING?

siveness and mathematical simplicity, is not a whit
inferior to the classical scheme of theoretical physics." 1

Let us come now to the personal story of Max Planck
himself. He was born at Kiel, Germany, on April 23,
1858. His father was Professor of Constitutional Law
at the University and was afterwards transferred to
Goettingen in the same capacity. The chief work
whereby his name is known is the Prussian Civil Code,
of which he is co-author. It is often said that the great
physicist has inherited certain qualities from his father,
especially the juridical faculty of sifting experimental
evidence, disentangling the significant from the mean-
ingless and probing to the absolute values hidden
beneath the relative. He has also a faculty for con-
structive clarity in building up a mathematical syn-
thesis. But perhaps the most striking quality which
he has derived from his early family associations is
shown in his attitude towards physical science as a
branch of human culture, forming an integral part
with the other branches of human learning and exer-
cising its influence on the destiny of humanity not
merely in a material way but even more deeply in a
spiritual way.

When Max Planck was seventeen years old he
entered the University of Munich, taking physics as
his chief subject. Three years later he went to Berlin
to complete his course at the University there. At that
time Helmholtz and Kirchhoff were the leading sci-

1 Die Naturwissenschaften, Vol. 26, p. 490.

INTRODUCTION

21

entific lights of the Prussian Capital. Kirchhoff was
Professor of Physics at the University and young
Planck read under him there, also attending the lec-
tures of Helmholtz and Weierstrass. He always asserts
that Kirchhoff was responsible for his keen interest in
thermodynamics, especially the famous Second Law. It
was on this subject that Max Planck wrote his treatise
for the doctorate, which he presented at the University
of Munich a year later, in 1879, when he received
the doctorate Summa cum Laude. The treatise was
entitled De secunda lege fundamentale doctrinae
mechanicae colons. Perhaps I ought to explain here
that in qualifying for the taking of degrees all uni-
versities in Germany are treated as one. A student may
take part of his course in one university and part in
another j so that, in case he should wish to follow
some special line of work in which there is an eminent
professor in some university away from his home town,
he can attend there and indeed make the rounds of all
the eminent professors if he likes, from one university
to another. The sum-total will be credited to him as if
he had studied at the one university all along.

Having received his doctorate, Max Planck became
a Privat Dozent at the Munich University. The Privat
Dozent is a university lecturer who receives fees but
no salary. In 1885 Planck was appointed Professor
of Physics at the University of Kiel and in 1889 he
came to Berlin as Professor Extraordinarius there. In
1892 he was appointed full professor in succession to
Kirchhoff at the University of Berlin. In 191 2 he

22 WHERE IS SCIENCE GOING?

became Permanent Secretary to the Prussian Academy
of Science. In 19 19 he received the Nobel Prize for
Physics. And in 1926 he became Professor Emeritus,
Schroedinger succeeding him in the Berlin Chair of
Theoretical Physics. In 1930 Adolf Harnack died and
Max Planck was elected President of the Emperor
William Society for the Advancement of Science,
which is the highest academic post in Germany.

What was it that first put Planck on the trail of the
quantum? That would be a rather long story to tell j
for the telling of it would involve an account of the
various attempts that were being energetically made
towards the end of the last century to solve the spec-
troscopic riddle of heat radiation. As this expression
may not convey a very clear idea to the mind of the
average reader, it will be well to explain it a little.

Everybody is acquainted with the solar spectrum,
which results in the breaking up of white light by
passing it through a prism, thus producing a spectrum
of colored rays which group themselves on the screen
and run continuously from red to violet. Newton was
the first to handle the phenomenon in a scientific man-
ner, and this led to the great problem of the nature
of light itself. In the case of heat radiation we have
a corresponding phenomenon. Sir William Herschel
was the first to show that the solar spectrum is not
confined to that part which is visible to the eye, from
the red to the violet. In 1 800 he discovered that there
are infra-red solar rays. By applying a thermometer to
the successive colors he discovered an uneven distri-

INTRODUCTION 23

bution of heat in the solar spectrum, the heat being
greatest below the red. This inequality had never
previously been suspected.

Now it is a matter of everyday experience that a
body when moderately heated gives out an invisible
radiation. The frequency of the undulations is too low
to influence the eye. As the temperature is gradually
increased, in a piece of iron, for instance, one might
expect that violet rays would first be perceptible, as
these have the minimum wave-length which is neces-
sary to stimulate the sense of sight. But that is not what
happens. The light is at first dull red, then bright red,
and finally becomes glowing white. Now the question
here is, how does the intensity of the rays of different
frequency change with the rising temperature? This
is what is called the problem of the spectral distribu-
tion of radiation for different temperatures. It is the
problem to which Max Planck devoted the first twenty
years of his academic career. In his address before the
Royal Swedish Academy of Science in Stockholm, on
the occasion of receiving the Nobel Prize, he said:

"Looking back over the past twenty years to the
time when the idea of the physical quantum of action,
and the measurement of it, first emerged into definite
shape from a mass of experimental facts, and looking
back beyond that over the long and labyrinthine path
which finally led to the discovery, I am vividly re-
minded of Goethe's saying that men will always be
making mistakes as long as they are striving after
something. During such a long and difficult struggle

24 WHERE IS SCIENCE GOING?

the researcher might be tempted again and again to
abandon his efforts as vain and fruitless, except that
every now and then a light strikes across his path
which furnishes him with irrefutable proof that, after
all his mistakes in taking one by-path after another,
he has at least made one step forward towards the dis-
covery of the truth that he is seeking. The steadfast
pursuance of one aim and purpose is indispensable to
the researcher and that aim will always light his way,
even though sometimes it may be dimmed by initial
failures.

"The aim which I had for so long before my mind
was the solution of the distribution of energy in the
normal spectrum of radiant heat. Gustav Kirchhoff had
shown that the nature of heat radiation is completely
independent of the character of the radiating bodies.
This pointed to the existence of a universal function
which must be dependent exclusively on temperature
and wave-length but in no way dependent on the
properties of the substance in question. If this remark-
able function could be discovered it might give a
deeper understanding of the relationship between
energy and temperature, which forms the main prob-
lem of thermodynamics and consequently of molecular
physics as a whole. At that time no way suggested itself
of discovering this function except to select from the
various bodies in nature certain kinds of bodies whose
capacities for emitting and absorbing heat are known
and then to calculate the heat radiation when the ex-
change of temperature is stationary. According to Kirch-

INTRODUCTION 25

hoff's theory, this must be independent of the nature
of the body itself."

He then traced in a modest and objective way the
rocky road that he had followed, the slips and falls by
the wayside, the discouragement, but always the per-
sistent effort and the determination to win through.
Finally the goal was reached, after a long journey of
twenty years.

Planck first presented the results of his discovery
in a communication to the German Physical Society,
on December 14, 1900. His paper was entitled "On
the Distribution of Energy in a Normal Spectrum."
The discovery of the function mentioned above had
been arrived at in the shape of a formula for measuring
radiant energy. He had experimented with what is
known as cavity radiation. This means that he heated
a hollow body to incandescence and allowed a beam
of radiation to issue through a small opening and
analyzed the beam in the spectroscope. In this way it
was found that radiant energy is not a continuous flow.
It is emitted in integral quantities, or quanta, which
can be expressed in integral numbers. In other words,
the measurement always results in integral multiples
of h v, where v is the frequency and h is a universal
constant, now known as Planck's constant. His greatest
triumph of technical skill was in deducing the value of
this constant to be 6.55 X io-27 erg-seconds. No radia-
tion can be emitted unless it is of at least that amount
or an integral multiple thereof. That is to say, our
stove cannot give us any heat until it has accumulated

26 WHERE IS SCIENCE GOING?

at least that amount. Then it will not increase the
radiation of its heat until it accumulates another in-
tegral packet which is exactly double that amount, and
so on. We can have 1 h v and 3 h v and 4 h v; but
we cannot have any fractional parts of h v. This in-
volved a revolutionary concept for radiation of heat,
and the concept was eventually shown to extend to all
radiation and finally to the interior structure of the
atom itself.

It soon became evident that Planck had brought to
light something that not merely explained the puzzle
of the spectrum of radiant heat but something that is
universally fundamental in nature. This was shown
by the gradual application of his theory in all directions.
Within a few years after its promulgation Einstein
applied the quantum theory to explain the constitution
of light and showed that light follows the same
process as heat radiation and is emitted in parcels or
quanta, called photons. Physicists in every country
began to practice the technique of "Quantizing" and
achieved very remarkable results. H. A. Lorentz, the
famous Dutch scientist, put the case thus in 1925:

"We have now advanced so far that this constant
(Planck's universal h) not only furnishes the basis for
explaining the intensity of radiation and the wave-
length for which it represents a maximum, but also
for interpreting the quantitative relations existing in
several other cases among the many physical quantities
it determines. I shall mention only a fewj namely,
the specific heat of solids, the photo-chemical effects

INTRODUCTION 27

of light, the orbits of electrons in the atom, the wave-
lengths of the lines of the spectrum, the frequency of
the Roentgen rays which are produced by the impact
of electrons of given velocity, the velocity with which
gas molecules can rotate, and also the distances be-
tween the particles which make up a crystal. It is no
exaggeration to say that in our picture of nature now-
adays it is the quantum conditions that hold matter
together and prevent it from completely losing its
energy by radiation. It is convincingly clear that we
are here dealing with real relations because the values
of h as derived from the different phenomena always
agree, and these values differ only by slight shades
from the number which Planck computed twenty-five
years ago on the experimental data that were then
available." 1

It is not the place here to attempt an explanation
of the scientific aspects of the quantum theory. The
reader will find several popular accounts — some of
them perhaps all too popular — of Planck's revolu-
tionary theory in various books on modern science.
My task here is rather to indicate the source from
which the material of this book has originated and try
to explain why it is that Planck has felt the need to
assert himself so strongly in dealing with certain philo-
sophical aspects of contemporary science. Most of the
essays here — the discussion on positivism and the dis-
cussion on determinism and free will — are outside the
sphere of pure physics. Why is it that the doyen of

1 Die Naturwissenschaften, Vol. 35, 1925, p. 1008.

28 WHERE IS SCIENCE GOING?

German physicists has felt himself called upon to take
so strong a stand?

A great deal has been written about the philosophical
implications of the quantum theory. Some of the physi-
cists declare categorically that the development of the
quantum theory has led to the overthrow of the prin-
ciple of causation as an axiom in scientific research.
Sir James Jeans puts this side of the question as
follows:

"Einstein showed in 19 17 that the theory founded
by Planck appeared, at first sight at least, to entail
consequences far more revolutionary than mere dis-
continuity. It appeared to dethrone the law of causation
from the position it had heretofore held as guiding
the course of the natural world. The old science had
confidently proclaimed that nature could follow only
one road, the road which was mapped out from the
beginning of time to its end by the continuous chain
of cause and effect; state A was inevitably succeeded
by state B. So far the new science has only been able
to say that state A may be followed by state B or C
or D or by innumerable other states. It can, it is true,
say that B is more likely than C, C than D, and so
on; it can even specify the relative probabilities of
states B, C and D. But, just because it has to speak
in terms of probabilities, it cannot predict with cer-
tainty which state will follow which; this is a matter
which lies on the knees of the gods — whatever gods
there be." 1

1 The Mysterious Universe, 1932, pp. 17 and 18.

INTRODUCTION 29

Further on Sir James Jeans states:

"Or again, to take another analogy, it is almost as
though the joints of the universe had somehow worked
loose, as though its mechanism had developed a cer-
tain amount of 'play,' such as we find in a well-worn
engine. Yet the analogy is misleading if it suggests
that the universe is in any way worn out or imperfect.
In an old or worn engine, the degree of 'play' or 'loose
jointedness' varies from point to point j in the natural
world it is measured by the mysterious quantity known
as 'Planck's constant hyy which proves to be absolutely
uniform throughout the universe. Its value, both in
the laboratory and in the stars, can be measured in
innumerable ways, and always proves to be precisely
the same. Yet the fact that 'loose jointedness,' of any
type whatever, pervades the whole universe destroys
the case for absolutely strict causation, this latter being
the characteristic of perfectly fitting machinery." 1

The italics are mine. Sir James Jeans's assertion is
illustrative of an attitude that is fairly common among
modern physicists. But it is an attitude to which Planck
is stoutly opposed. Scientifically considered, it is pre-
mature $ and, logically considered, it is too much of
a jump towards a sweeping conclusion. Planck would
claim, and so would Einstein, that it is not the prin-
ciple of causation itself which has broken down in
modern physics, but rather the traditional formulation
of it. The principle of causation is one thing $ but the
way in which it was formulated by Aristotle and the

1The Mysterious Universe, 1932, p. 24.

30 WHERE IS SCIENCE GOING?

Scholastics and Newton and Kant is quite another
thing. As applied to happenings in nature, whether in
the sphere of mind or of matter, the traditional formu-
lation must be considered rather too rough-and-ready.
In the discussion appended to this book the latter point
will be examined somewhat more sharply. What is of
chief interest here is to ask why Planck considers the
causal controversy of so much importance that he
spends a considerable portion of his time to-day — and
he is a very busy man — in the delivery of lectures and
the writing of essays on it. Why does he assert him-
self so emphatically on this point? The answer cannot
be that he is a stickler for the authority of tradition 5
because, as a matter of fact, he has headed the greatest
revolt in modern science. The answer therefore must
be looked for in a different direction.

At the present time there is a wave of public inter-
est in physical science. It arose immediately after the
war and shows no signs of receding. This is undoubt-
edly due to the fact that physical science is the most
vital expression of the higher activities of human
thought to-day. Moreover the metaphysical content of
the higher speculations in theoretical physics seems to
be the favorite modern pabulum for the soul-hunger
which was formerly appeased by the ideals of art and
religion. From many points of view, this may be a
fortunate thing ; but from other points of view it may
be a misfortune, especially from the scientific point of
view. Edwin Schroedinger has recently published a
brilliant essay (Ist die Naturwissenschaft Milieube-

INTRODUCTION $i

dingt? Barth, Leipzig, 1932) in which he suggests
that physical science has fallen a victim to the Zeitgeist.
To-day the Umsturzbedürfnis (The need for some-
thing radically different from the established order)
is a universal feature of our civilization. The authority
of tradition is a drawback rather than a recommenda-
tion in the case of principles or methods hitherto domi-
nant in art or music or even politics and business. And
we find this same devaluation influencing scientific
ideas. When Einstein promulgated his relativity theory
much of the enthusiasm with which it was proclaimed
was associated with the impression that it constituted
a complete overthrow of Newtonian doctrines ; whereas,
as a matter of fact, relativity is an expansion and re-
finement of Newtonian physics. And so when Heisen-
berg proclaimed his Principle of Indeterminacy it was
almost immediately interpreted, even among physicists
themselves, as definitely effecting an overthrow of the
causation principle. As a matter of fact, we have no
means whatsoever of proving or disproving the ex-
istence of causation in the external world of nature.
And the aim which Heisenberg had before his mind
in formulating the Principle of Indeterminacy was to
find a rule whereby we can deal with minute processes
in natural phenomena, such as those in which the
elementary quantum of action is involved. Here the
causal principle is not applicable. That is to say, we
cannot estimate simultaneously both the velocity and
position in time-space of a particle and say where it
will be a moment hence. But this does not mean that

32 WHERE IS SCIENCE GOING?

the causal sequence is not actually verified objectively.
It means that we cannot detect its operation j because,
as things stand to-day, our research instruments and
our mental equipment are not adequate to the task.
The Principle of Indeterminacy is in reality an alter-
native working hypothesis which takes the place of the
strictly causal method in quantum physics. But Heisen-
berg himself would be one of the first to protest
against the idea of interpreting his Principle of Inde-
terminacy as tantamount to a denial of the principle
of causation.

Why is it then that this hasty conclusion is so much
in vogue? It is probably due to two things: First the
Zeitgeist. The spirit of the age does not want to be
considered the heir of the old order and wants to
consider itself free from all laws handed down through
the authority of tradition. Secondly, the standardization
of modern life, with its mass production and high-
powered salesmanship and advertisement and transport
and mass housing and insurance undertakings, etc., has
evolved a system of statistical rules which are true
when masses of events are concerned, though they are
not at all applicable to the individual. People call this
the principle of statistical causality. Physicists have
brought it over into their science and often speak of
it as the opposite of strict causation in the classical
sense. They speak of statistical causation as opposed to
dynamical causation. But, as a matter of fact, statis-
tical causality and even what are called the laws of
probability are all based on the presupposition of strict j

INTRODUCTION 33

causation in the individual cases dealt with. According
to the statistical causality principle of insurance com-
panies, so many thousand people die of certain diseases
in the year, at certain ages and in certain professions.
It is on the basis of these statistics that insurance poli-
cies are drawn up. But these statistics have nothing to
do with the actual cause of death in the case of the
individual insured.

Now, anybody who has the interests of his own art
or science at heart will strive to protect it against adul-
teration through the intrusion of principles and methods
which are foreign to it. That is exactly Planck's posi-
tion in regard to physical science. If we are living
at a time that is breaking away from the old political
and social traditions, this is fundamentally because the
old traditions are not suitable to the changed economic,
and therefore social, order in which we live. But
scientific research is something that has to be carried on
apart from the changing circumstances of human ex-
istence. It is natural, of course, that the public mind
should turn to that branch of our spiritual culture
which is the most vital to-day, namely physical science,
and seek in it a foint d'appui for the general world-
outlook. But this very fact alone, flattering as it may
be for the individual scientist, endangers the integrity
of the science in question.

It is from this source that Planck's interest in the
causality controversy arises. And it is in this light too
that we are to view his attitude towards the positivist
thesis. The undue popularization of physical science

34 WHERE IS SCIENCE GOING?

has probably tempted some physicists hastily to build
up a theoretical structure wherein the public mind may
find a congenial object of awe and wonderment and,
in a sense, worship, such as in former days was sup-
plied by the mysteries of religion. This may explain
that phase of modern theoretical science which some-
what resembles the sophist phase into which Greek
philosophy degenerated and which also characterized
the decadence of the scholastic movement. It was this
latter decadence that instigated the founding of the
empiricist school in England at the time of Locke, for
the purpose of reconstructing a reliable basis of philo-
sophic thought. We have a similar movement in physi-
cal science to-day, with a similar purpose in view.
There are some physicists who would reduce the scope
of physical science to a bald description of the events
scientifically discovered as occurring in nature, and
would entirely exclude all theory and hypothesis-
building. Planck feels that this restriction of scope is
anti-scientific and very much to the detriment of
physics. That is why he is so stoutly opposed to it. As
the doyen of international physicists he feels within
his rights in taking up the cudgels against the renun-
ciatory movement. That he voices the mind of leading
German scientists in this regard I am quite convinced.
Not long ago I happened to be at dinner with a num-
ber of Planck's colleagues at Goettingen. Hermann
Weyl was there, and Max Born, and James Franck. i
Planck was mentioned a great deal and there was some I
rather lively discussion about his intransigence on the

INTRODUCTION 35

causation principle, but one and all agreed in cham-
pioning his stand against the positivist teaching.

As this is a sort of close-up sketch, for the purpose
of bringing the personality of the author of the
quantum theory vividly before the mind of the reader,
I shall conclude with a few remarks on Planck's per-
sonal standing among his colleagues. He is undoubtedly
the most popular figure in the academic world of Ger-
many. Indeed one may say without the slightest fear
of exaggeration that he is the beloved of his colleagues.
Professor Sommerfeld of Munich, whose name is also
renowned in the realm of quantum physics, wrote of
Planck some time ago: "His doctor's diploma (in
1879) bore the superscription Summa Cum Laude. We
would write the same superscription over his work
during the whole fifty years that have elapsed since
then, and not for his scientific work alone but also for
his human example. He has never written a word that
was not genuine. And in polemical questions he has
always been chivalrous to his opponent. When the Ger-
man Physical Society was being reorganized there was
dissension and antagonism; but Planck was the trusted
representative of both sides, the naturally fair-minded
arbiter."

Sommerfeld tells a story about Planck that is illus-
trative of the unselfish and modest manner in which
he is always ready to collaborate with his colleagues.
Sommerfeld was once engaged on some research con-
cerning what is known as Phase-space in atomic
physics. He wrote to Planck for assistance and Planck

36 WHERE IS SCIENCE GOING?

immediately placed at his disposal the results of his
own experiments in the same field. Sommerfeld fell
into a poetical strain and sent a couplet to Planck in
which he explained that he himself was only putting
forth a humble endeavor to gather a few flowers in
the great new land of quantum physics which Planck
had turned from an unknown wilderness into arable
ground.

Der sorgsam urbar macht das neue Land

Dieweil ich hier und da ein Blumenstraueschen fand.

To this delightful compliment Planck replied with a
quatrain in a still more gentle spirit.

Was Du gefflueckt, was ich gefflueckt
Das wollen wir verbinden^
Und weil sich eins zum andern schickt
Den sc ho ens ten Kranz draus winden.

(What you have picked and I have picked,
These we shall bind together.
Entwining thus a fair bouquet
From gifts we send each other.)

In the modest little account which Planck gave of
himself before the Royal Swedish Academy on the
occasion of receiving the Nobel Prize, he mentioned
a tragedy which has afflicted his family life. This was
the loss of his two daughters, both of whom died soon
after marriage, one might almost say in their bridal
robes, and the loss of a very gifted son in the war.
Another son was wounded but has survived and is
now a Minister in the von Papen Cabinet.

INTRODUCTION 37

When conversing with Planck even on scientific sub-
jects one often feels that this tragedy of his children
has made a deep impress on his soul. The memory of
it seems to evoke a certain wistful quality which is
profound in his nature and gives it the warmer glow
that one is inclined to call mystic. And indeed, though
a scientist and a perfectly practical man of the world
and an up-to-date gentleman in manner and dress and
also a sportsman, who climbed the Jungfrau to cele-
brate his seventy-second birthday a few years ago —
still one often thinks of him in conjunction with
Beethoven, I don't know why, and one remembers
that at the beginning of Planck's career there was a
question whether he would develop the musical side
of his genius or the scientific side. He developed the
latter. But he could not develop the one without en-
riching the other also, because the pursuit of theoretical
science demands as its first prerequisite the construc-
tive imagination of the artist. And the constant seeking
after nature's harmonies responds to the longing for
musical expression. Anyhow it is a significant fact that
the two greatest scientists in Germany, Einstein and
Planck, are musicians also.

On visiting his home in the Wangenheimer Strasse,
Berlin, and chatting with him in that big room which
is at once his reception parlor and study, I often think
that his own private trials have been sublimated by the
tragedy of his country and this in its turn sublimated
by the universal tragedy of the modern world. For on
this he broods more than most busy men do. But the

38 WHERE IS SCIENCE GOING?

moment the first cloud of depression shows itself he
counters it with his favorite motto, Man muss optimist
sein. We must be optimists. He has said that the in-
scription on the gate of the temple of science indi-
cating the condition on which alone her devotees may
enter, is: Ye must have Faith. Running through all his
work and all that he has said or says there is always
this golden thread of a living faith in the ultimate
purposes of creation.

WHERE IS
SCIENCE GOING?

CHAPTER I
FIFTY YEARS OF SCIENCE

HERE I shall give a short sketch of physical science
in Germany during the period of my own active
work in that field. For the sake of clarity it will be better
if we ignore the chronological sequence of events and try
to trace the main lines along which the various specific
groups of ideas have developed. While doing this I shall
take into account also the cooperative work done by
scientists in other countries. And if I mention certain
names, while leaving out many others quite as eminent if
not more so, these names will be cited merely as land-
marks to indicate a particular stage or turning-point,
without any suggestion whatsoever of making a personal
valuation of the work done by the scientist mentioned.

Let us take the year 1 8 80 as our starting-point. At that
time four great names shone out above all others to
illuminate the direction along which physical inquiry was
advancing. These were: Hermann von Helmholtz,
Gustav Kirchhoff, Rudolf Clausius and Ludwig Boltz-
mann. The two former were the chief luminaries in the
contiguous provinces of mechanics and electrodynamics,
while the two latter were prominent in the associated
spheres of thermodynamics and atomic physics. But there

41

42 WHERE IS SCIENCE GOING?

was really no dividing space between the activities of
those four pioneers. They represented a concept of the
physical universe which was common to them all and
towards which their attitudes were in the closest harmony.
That common concept rested on a twofold foundation.
One part of the foundation consisted of Hamilton's
Principle of Least Action, which includes the Principle
of Conservation of Energy. The second part of the
foundation represented the Second Law of Thermo-
dynamics.

At that time it was considered by all physicists as prac-
tically certain that any subsequent development in
theoretical physics must necessarily be in the direction of
working out those two universal principles to their final
conclusion and application. Nobody then dreamt that
within a short period of time the two principles which
stood so proudly alone in supporting the structure of
physical science would have to take other principles into
partnership on an independent and equal footing.

The advent of these new principles was already fore-
shadowed in some of the ideas put forward by the older
pioneers whom I have mentioned and also in the tenden-
cies of those who then represented the rising generation.
Heinrich Hertz was the most outstanding among the lat-
ter. He stands at the opening of the new era and it would
be impossible to overestimate his services to the cause of
modern physics. Unfortunately his work was cut short
by an early death, at the age of thirty-four, while he was
still active as Professor of Theoretical Physics at the
University of Bonn. Despite his epoch-making discovery

FIFTY YEARS OF SCIENCE 43

of the propagation of electromagnetic waves through a
vacuum, Hertz was not the founder of a new scientific
doctrine. What he achieved was to bring an already exist-
ing theory to its completion, for he finally established the
Maxwell theory of light and thus displaced all the various
other theories which for a long time had been struggling
against one another for precedence in the field of electro-
dynamics. By reason of these achievements Hertz must
be credited with the accomplishment of a very important
advance towards the unification of theoretical physics, for
he thus brought optics and electrodynamics under the one
doctrinal discipline.

His last work was the simplification of Newtonian
mechanics to an ideal degree. In Newtonian mechanics
the distinction had always been drawn between kinetic
and potential energy as essentially different entities.
Hertz succeeded in unifying this bipartite concept, which
he did by fundamentally eliminating the idea of a force.
The Newtonian force was identified by Hertz with in-
ternal motion in matter, so that what had hitherto been
called potential energy was now replaced by the kinetic
concept. Hertz however never attempted to explain the
nature of these inner motions in any particular direction,
such as gravitation for instance. He contented himself
with establishing in principle the hypothesis of unifica-
tion.

If we make allowance for certain theories that were
still only in what may be called a rudimentary stage of
development, we can say that at the end of the last cen-
tury the science of theoretical physics as a whole presented

44 WHERE IS SCIENCE GOING?

the imposing aspect of a complete and perfectly articu-
lated structure. A penetrating observer however could
not have failed to notice that in some sections of the
foundation there were open flaws which could not be
looked upon with anything like satisfaction. Hertz did
not fail to see this. And he did not fail to call attention
to the fact that the integration of the structure here would
prove at least very difficult if not impossible. These flaws
soon became the object of attack on the part of scientific
criticism. And this criticism developed into a creative
movement which eventually brought about the most im-
portant expansion that theoretical physics has experienced
since the time of Newton.

No doctrinal system in physical science, or indeed per-
haps in any science, will alter its content of its own accord.
Here we always need the pressure of outer circumstances.
Indeed the more intelligible and comprehensive a theo-
retical system is the more obstinately it will resist all at-
tempts at reconstruction or expansion. And this is because
in a synthesis of thought where there is an all-round logi-
cal coherence any alteration in one part of the structure is
bound to upset other parts also. For instance, the main
difficulty about the acceptance of the relativity theory was
not merely a question of its objective merits but rather the
question of how far it would upset the Newtonian struc-
ture of theoretical dynamics. The fact is that no alteration
in a well-built synthesis of thought can be effected unless
strong pressure is brought to bear upon it from outside.
This strong pressure must come from a well-constructed
body of theory which has been firmly consolidated by

FIFTY YEARS OF SCIENCE 45

the test of experimental research. It is only thus that we
can bring about the surrender of theoretical dogmas
hitherto universally accepted as correct. And thus only
can we succeed in forcing a fundamental revision of the
whole doctrinal structure. Following a reconstruction of
this type there invariably arises a fresh series of problems
for experimental research to tackle. It is in the tackling
of these problems that new ideas are suggested which
subsequently lead to the formulations of further theories
and hypotheses.

This alternative play of theory and experiment, of
theoretical constructions on the side of abstract reason and
the testing of these by their application to objective
reality, is a special characteristic of modern physics. In-
deed it is of enormous significance in all scientific prog-
ress, for it is the one safe and sound source from which
reliable and enduring results can be produced.

There were two problems of theoretical physics which
may be said to have absorbed almost the whole of Hertz's
attention towards the end of his life. But they defied all
his attempts at solution. And these two problems eventu-
ally became the nucleus out of which the physics of our
day have developed. These problems were: (i) the
nature of the cathode rays, and (2) electrodynamic
motion. Each of these two problems has its own history -y
for each furnished the starting-point of an independent
development. The former led to the theory of electrons,
the latter to the relativity theory.

46

WHERE IS SCIENCE GOING?

THE ELECTRONIC THEORY

The cathode rays were first discovered by von Pleucker
in the year 1859. This discovery naturally opened the
question as to the nature of the rays themselves. Were
they the carriers of electric charges or were they undula-
tory, like the rays of light? The fact that the X-rays could
not be deflected by bringing a magnet to bear on them
seemed to point to their electrical character. But Hertz
decided in favor of the opposite view. He came to this
conclusion after numerous experiments in which he had
tested the cathode rays by bringing them to bear on a
magnetic needle and found in each case that the needle
remained in its position of equilibrium. Hertz accord-
ingly was inclined to identify the cathode rays with the
waves of light-ether, which scientists had for a long time
been vainly trying to discover. If Hertz were right here
his theory would mean that one of the awkward voids in
the structure of theoretical physics would thus be filled in.

But, contrary to Hertz's suggestion, there were indica-
tions which pointed to the assumption that the cathode
rays are corpuscular and the carriers of electric charges.
With the advance of experimental methods scientists be-
gan to believe more and more that the cathode rays would
eventually be found to be the carriers of negative elec-
tricity. Indications pointed definitively in this direction
once W. Wien had discovered the electric charge in the
rays and D. Wiechert their velocity. Therewith the
foundation of the electronic theory was laid.

It is interesting to note how in this case theory and

FIFTY YEARS OF SCIENCE 47

experiment worked hand in hand, one taking the leader-
ship to-day and the other to-morrow. Experiment first
appears in the lead, represented especially by Philippe
Lenard. In 1892 he showed that the cathode rays could
pass through very thin metal foils and he succeeded in
obtaining them outside the tube in which they were gen-
erated. Later on the experimental impulse produced a
marvelous and unexpected result, in 1895, when W.
Roentgen, while working on the cathode rays, discovered
the X-rays and thus with one blow opened up a new
kingdom for physical science. At the same time his dis-
covery placed a completely new task before the theoret-
ical physics of the time. This led indirectly to the
discovery of uranium rays on the part of the French
physicist, Henri Becquerel. A further development in
the same experimental field eventuated in the discovery
of the radioactive substances and the establishment of
the theory of radioactivity, on the part of Rutherford
and Soddy.

Experimental investigation into the nature of the
various phenomena connected with cathode rays and
X-rays and radioactivity progressed on all sides. The
special problem to be solvea was that of their origin and
the nature of their activity. But the Roentgen rays for a
long time absolutely defied all attempts at quantitative
analysis. In the early experimental stages it was readily
established that the X-rays were of an electromagnetic
nature, through the fact that when we put a piece of
metal opposite the cathode inside the tube — the so-called
anti-cathode — streams of electrons are shot off from the

48 WHERE IS SCIENCE GOING?

anti-cathode. Yet it was for a long time impossible to
arrive at any satisfactory results in measuring the wave-
length of the X-rays. Here it was that the work of a
theorist, Professor von Laue, opened the way for the
next decisive step.

In the year 19 12 von Laue in collaboration with the
experimental physicists, W. Friedrich and P. Kipping,
succeeded in ascertaining the wave-length of the X-rays
by passing them through crystalline media and thus
bringing about the phenomena of interference. In this
way it was found possible to measure the wave-length,
but the experiment holds good of course only for homo-
geneous Roentgen rays, because otherwise confusion
would arise from the various interference positions over-
lapping one another.

Von Laue's discovery turned out quite as valuable in
the sphere of atomic physics as in the sphere of optics.
It enabled physicists definitely to classify the Roentgen
rays and the Gamma rays with the radioactive substances
in electrodynamics. On the other hand, the carriers of the
cathode rays — that is to say, the free electrons — with
their relatively small mass, proved to be something en-
tirely new to physical science. It was the introduction of
these electrons that made it possible to understand various
physical phenomena which hitherto had remained in the
region of mystery.

As far back as 1881 Helmholtz pointed out, in his
famous Faraday lecture, that from the standpoint of
chemical atomics the empirically deduced laws of chemi-
cal decomposition by galvanic action could be explained

FIFTY YEARS OF SCIENCE 49

only in case we attribute an atomic structure to electricity
as well as to matter. The atom of electricity postulated by
Helmholtz first appeared in the cathode rays, free and
detached from all matter, and was again located in the
Beta rays of radioactive substances. In contradistinction
to chemical atoms, all electric atoms are found to be
uniform and to differ from one another only in their
velocity. The discovery of electrons and the introduction
of them into the scientific picture of the universe threw a
new light on the nature of metallic conduction. It is well
known that an electric current when passing through a
metal conductor, such as an ordinary piece of copper wire,
produces no chemical change. Once the existence of elec-
trons became known it seemed natural to consider these
free electrons as carriers of the electric current through
the metal. This opinion, which had previously been put
forward by Wm. Weber, was now revived and further
developed by E. Riecke and P. Drude.

Once the free electrons had been accepted by physical
science as veritable factors in nature, an attempt was made
to prove that these electrons also existed in a "bound"
condition. This attempt put the investigators on the track
of a whole new series of physical and chemical properties
of matter. P. Drude explained the optical dispersion and
chemical valency of a substance by referring these to the
electrons in the atoms and for this purpose he differen-
tiated between firmly bound and loosely bound electrons.
The former cause dispersion of light and the latter ac-
count for the property of chemical valency. Subsequently
H. A. Lorentz formulated the whole electronic theory

50 WHERE IS SCIENCE GOING?

as a complete and independent synthesis. His special
endeavor was to ascertain if and how far all material
constants of a substance can be accounted for by the
arrangement and interaction of the atoms and electrons
contained in them.

Taking the results thus obtained, together with the
work done in the sphere of radioactivity, the final conse-
quence of the researches which were directed towards
discovering the inner constitution of matter within the
past fifty years is the knowledge that all matter is made
up of two primordial elements: negative electricity and
positive electricity. Both consist of uniform minute par-
ticles containing uniform but opposite charges. The posi-
tive particle, which is the heavier, is called the proton and
the negative, the lighter, is called the electron. The union
of both is called the neutron. Every electrically neutral
chemical atom is made up by a certain number of protons
held fast together and by an equal number of electrons of
which some are bound to the proton and form together
with it the nucleus of the atom, while the others — that
is to say, the free electrons — move in orbits around the
nucleus. The number of these latter, which are called free
or orbital electrons, gives in each case what is called the
atomic number. It is on this number that all the chemical
properties of the various elements depend.

THE RELATIVITY THEORY

I have spoken at length of Hermann Hertz and his
work in the movement which eventually led to the es-
tablishment of the electronic theory. Now we come to the

FIFTY YEARS OF SCIENCE 51

second great theory which I have mentioned as forming,
with the electronic theory, one of the twin principles
which were entirely undreamt of fifty years ago and are
now among the main piles supporting the scientific struc-
ture. This second principle is the relativity theory. And
here again we find that Hertz was among the pioneers.
The last and most fruitful period of his life's work was
devoted largely to the study of electrodynamic phenom-
ena in moving bodies. In this work Hertz chose as his
starting-point the principle that all movement is relative.
Adopting Maxwell's theory as his groundwork, he for-
mulated for the phenomena of electrodynamic move-
ment a system of equations in which the velocity of the
bodies concerned is taken only in a relative sense. This is
expressed by the fact that the equations, just as the New-
tonian laws of motion, remain unchanged if the velocity
of the body in question be taken in relation to a moving
reference system or, in other words, a moving observer.
There is no necessity in the Hertzian theory to introduce
the idea of a special substantial medium of transmission
for the electrodynamic waves. If we should think of in-
troducing ether as a substantial medium of transmission
here, then we must assume that it has no independent
motion of its own in relation to matter but is completely
carried forward with it.

The Hertzian theory was excellent in its inner coher-
ence, but from the beginning he recognized that it had
considerable drawbacks. A wave of light passing through
air which is also in motion must be considered in conjunc-
tion with the movement of the air, just as in the case of

52 WHERE IS SCIENCE GOING?

sound waves, no matter how rarefied the air may be. This
was a necessity of the Hertzian theory but it was con-
tradicted through a decisive discovery made by Fizeau,
who proved that light passes through moving air with
just the same velocity as through still air. In other words
it goes against the wind or in a perfect calm or with the
wind at the same rate of speed.

H. Lorentz endeavored to smooth out this contradic-
tion between the Hertzian theory and Fizeau's discovery
by putting forward the idea of a stationary ether permeat-
ing the whole of space. This was suggested as the carrier
and transmitter of all electrodynamic action. In this ether
the atoms and electrons move about as distinct particles.
Thus the advantages of Hertz's theory were retained and
at the same time the theory could be harmonized with
Fizeau's findings. On the other hand, however, this in-
volved the renunciation of the idea of relativity ; because
it established a definite object of reference absolutely at
rest. This was a static ether and the hypothesis of its
existence seemed more satisfactory than any that had
hitherto been put forward.

The relativity principle in this way received a setback.
But reprisals were soon forthcoming, inasmuch as new
defects arose which the Hertzian theory could not cope
with. All attempts to measure the absolute velocity of the
earth had failed. In other words it turned out impossible
to measure the velocity of the earth in relation to
the hypothetically static ether. Even the most delicate
of all experiments, namely that carried out by Michelson
and Morley, could detect no trace whatsoever of the in-

FIFTY YEARS OF SCIENCE 53

fluence of the earth's motion on the velocity of light
although, according to the Lorentzian doctrine, this
should have made itself felt.

Under these circumstances theoretical physics, at the
end of the last century, was faced with the alternative
of renouncing either the remarkably useful Lorentzian
theory or the theory of relativity. The crisis came into
public notice very strikingly at a meeting of the Society
of German Physicists and Physicians,1 which was held at
Dusseldorf in the August of 1898. On that occasion the
whole question was discussed in a debate which centered
around two papers that were read there ; one by W. Wien
and the other by H. A. Lorentz. The controversy re-
mained open for seven years. Then, in the year 1905, a
solution was put forward by Albert Einstein in his Theory
of Relativity. The Einsteinian hypothesis allowed the
Lorentzian theory to stand, but only at the cost of intro-
ducing what at first sight appeared to be an entirely alien
hypothesis, namely, that the dimensions of time and space
cannot be taken independently of one another but must
be welded together when there is question of the velocity
of light in vacuo. This hypothesis was logically unassail-
able, because it was expressed in a mathematical formula-
tion that was flawless in itself. Yet the relativity thesis
completely contradicted all hitherto accepted opinions.

Only a few years after Einstein had published his first
presentation of the relativity hypothesis Minkowski suc-
ceeded in bringing a corroborative light to bear on the
suggestion. He showed that if we look upon time as

1 Gesellschaft deutscher Naturforscher und Aerzte.

54 WHERE IS SCIENCE GOING?

something imaginary and assume the unit of time to be
the amount of time which a beam of light takes to travel
over the unit of length, then all our electrodynamic equa-
tions in relation to space and time will be symmetrical ;
because the one dimension for time and the three dimen-
sions for space enter as factors on an equal footing in the
formulation of every law of electrodynamics. Thus the
three-dimensional "space" is expanded into the four-
dimensional "world" and the mathematical laws that
govern the whole field of electrodynamics remain in-
variable when the reference system — that is to say, the
observer — changes its velocity, just as they remain in-
variable when the reference system changes its motion
from one direction to another.

Now the next question to arise was this: If the relativity
hypothesis in its new formulation is to have meaning and
validity for physical science as a whole, it must apply not
merely to electrodynamics but also to mechanics. If, how-
ever, the relativity theory be applicable and valid in the
field of mechanics, then we must change the laws of
motion formulated by Newton 3 because the Newtonian
laws do not remain constant when the four-dimensional
reference system is changed. Out of these problems arose
what is called relativist mechanics, which are an expansion
and refinement of Newtonian mechanics. The theory of
relativist mechanics was verified by experiment in the
case of rapidly moving electrons, for this experiment
showed that mass is not independent of velocity. In other
words it was shown that the mass of a rapidly moving
body increases with the increase of velocity. And thus a

FIFTY YEARS OF SCIENCE 55

further corroboration of the Einstein hypothesis was
provided.

Beyond the achievement of welding space and time
together with the mechanical laws of motion, the rela-
tivity theory accomplished another and no less important
amalgamation. This was the identification of mass with
energy. The unification of these two concepts establishes
for all equations in physical science the same kind of
symmetry as the four coordinates of the space-time con-
tinuum, the momentum vector corresponding to the place
vector and the energy scalar corresponding to the time
scalar. Another important consequence of the relativity
theory is that the energy of a body at rest is given a quite
positive value, which is expressed through the multipli-
cation of its mass by the square of the velocity of light ;
so that in general mass is to be considered under the
concept of energy.

But Einstein did not rest content with this success of
his theory. Once it had been shown that all reference sys-
tems, or standpoints of observation, are equally valid as
long as they are interchanged with one another through
linear rectangular transformation, Einstein was led to ask
whether and how far such an equivalence would hold
good for a quite arbitrary reference system. The trans-
formation of simple mechanical equations to any other
reference system generally involves certain additional
factors such as that of a centrifugal force where there is
question of a rotating reference system, such as the earth,
and these additional factors appear as the effect of gravity
in so far as ponderable mass is identified with inertial

56 WHERE IS SCIENCE GOING?

mass. Now the hypothesis that, from the viewpoint of
physical science, no geometrical reference system has
from the outset any advantage over any other system,
and that the property of invariance can be explained only
on the basis of the Riemann fundamental tensor — which
on its part depends on the distribution of matter in space
— led to the formulation of the general relativity theory.
This general theory of relativity includes the former
theory as a special case and holds the same relation to the
special theory of relativity as Riemann's geometry holds
to Euclid's geometry.

The practical significance of the general theory of
relativity is naturally confined to very powerful gravita-
tional fields such as that of the sun, whereby the color
and the light are affected, or to movements which have
secular periods, such as the perihelion displacement of
the orbit of Mercury. The general theory of relativity
represents the first great step towards the ideal goal of
geometrizing the whole of physics. Einstein has recently
devoted himself to the task of opening the way for the
second step, which would unite mechanics and electro-
dynamics under the one system of equations. To this end
he has undertaken the task of formulating a single field
theory, based on a different geometry from that of
Riemann. We have yet to await the final success of this
attempt.

THE QUANTUM THEORY

Apart from and quite independent of the relativity
theory, the quantum theory has given a new impress to

FIFTY YEARS OF SCIENCE 57

theoretical physics during the past thirty years. Just as in
the case of the relativity theory, its origin and foundation
arose from recognition of the fact that the old classical
theory had to be abandoned because it failed to explain
results which had been established through experimental
means. These results, however, were not obtained in the
region of optics but rather in that of thermodynamics and
arose from the measurement of radiant energy in the
emission spectrum of black bodies.

According to the Kirchhof? law this radiant energy is
independent of the nature of the radiating substance and
therefore has a universal significance. In this direction
indeed the classical theory had already led to important
results. In the first place L. Boltzmann deduced from
Maxwell's discoveries in regard to the pressure exerted
by radiation, and from the laws of thermodynamics, the
dependence of all types of radiation on temperature. W.
Wien extended the same principle further and showed
that the curve of the distribution of energy on the spec-
trum, especially in its location and maximum extent, is
displaced by a change of temperature. This was in full
harmony with the most delicate measurements. But in
relation to the shape of this curve there resulted a very
strong discrepancy between the conclusions arrived at
theoretically and the measurements carried out by von
Lummer and Pringsheim, Rubens and Kurlbaum. Then
Max Planck, taking the laws of thermodynamics as the
basis upon which an explanation of the experimental re-
sults could be obtained, arrived at the revolutionary
hypothesis that the manifold features which an oscillating

58 WHERE IS SCIENCE GOING?

and radiating picture possesses are complete entities in
themselves and that the difference between any two fea-
tures of the picture is characterized by a definite universal
constant, namely the elementary quantum of action.

The establishment of this hypothesis involved a funda-
mental break with the opinions hitherto held in physical
science ; because until then it had been an accepted dogma
that the state of a physical picture could be indefinitely
altered. The fruitfulness of the new hypothesis showed
itself immediately in the fact that it led to a law which
explained the distribution of energy on the spectrum and
was in perfect harmony with the measurements. But it
also supplied a means for determining the absolute
weights of molecules and atoms. Up to then, in so far as
atomic realities had been measured at all, science had to
be content with more or less rough estimates. Einstein
readily showed that the new theory had a further conse-
quence inasmuch as it applied to the energy and specific
heat of material bodies. Hitherto it had been only a mere
supposition that specific heat decreases illimitably with
decrease of temperature, but this now became established
by experimental proof. Max Born and Th. von Karman,
on the one hand, and P. Debye, on the other, began to
study carefully from the standpoint of the quantum
theory the problem of the dependence of specific heat on
temperature, and succeeded in formulating a law accord-
ing to which it is possible to reckon the variation of specific
heat with temperature from the elastic constants of the
substance in question. The most striking proof, however,
for the universality of the quantum of action is to be

FIFTY YEARS OF SCIENCE 59

found in the circumstance that not only the whole of the
heat theory put forward by W. Nernst in the year 1906,
independently of the quantum theory, is in harmony with
the quantum theory, but also that the chemical constant
introduced by Nernst depends on the quantum of action.
This was clearly demonstrated by O. Sackur and H.
Tetrode.

Belief in the soundness of the quantum theory has
nowadays become so strong and widespread that if the
measurement of a chemical constant does not tally with
the theoretical reckoning the discrepancy is attributed,
not to the quantum theory as such, but to the manner of
its application, namely the assumption of certain atomic
conditions in regard to the substance in question. But the
laws of thermodynamics are only of a summary and
statistical nature and can give only summary results when
applied to electronic processes in the atom. Now if the
quantum of action has the significance which has come
to be ascribed to it to-day in thermodynamics it must make
itself felt also in every single process within the atom, in
every case of emission and absorption of radiation and in
the free dispersion of light radiation. Here it was Einstein
once again who formulated the hypothesis that the light
quanta have an independent existence and exercise an in-
dependent activity.

This led to the putting forward of a whole series of
new questions and started correspondingly new investi-
gations in physics and chemistry. These dealt with the
emission of light quanta on the one hand and with elec-
trons, atoms, and molecules, on the other. The first

6o WHERE IS SCIENCE GOING?

direct measurement of the quantum of action was ob-
tained by J. Franck and G. Hertz by liberating quanti-
ties of light through electronic impulses. Niels Bohr
succeeded in further elucidating the theory and extended
its application beyond the thermodynamic sphere. On
the basis of the quantum he was able to lay down the
laws which are followed by the minute activities taking
place in the interior world of the atom. By the construc-
tion of his atom model he showed mathematically that
if the electrons of the atom be held to revolve at enor-
mous speeds, the change of energy involved in the dis-
placement of an electron from one orbit to another
exactly corresponds to the quantum theory that the
variation of the physical state does not take place gradu-
ally but in integral jumps. This was the first time that
the quantum theory came to be applied outside of the
region of thermodynamics.

The quantum way of solving physical problems was
further extended by A. Sommerfeld, who in this manner
succeeded in solving the riddle of delicate spectral
structures which had hitherto defied explanation. Inde-
pendently entirely of spectral phenomena, the Bohr
model of the atom proved effective in the elucidation of
chemical laws, including those underlying the periodi-
cally occurring functions of elements in chemical
structures.

Professor Bohr himself has never claimed that his
model of the atom provides the final solution of the
quantum problem ; but the correspondence principle
which he introduced has proved remarkably fruitful

FIFTY YEARS OF SCIENCE 61

because, in combination with the classical theory, it
points out the direction for the further development of
the quantum theory.

In point of fact a certain amount of uncertainty
lingered on because the discontinuous character of the
Bohr atom, the so-called stationary electron orbits, did
not accord in their peculiarities with the laws of classical
mechanics. Professor Heisenberg discovered a way out
of this difficulty by formulating a detailed description of
electronic motion in a sense entirely foreign to classical
theories. He showed that only dimensions which in prin-
ciple were directly measurable should be treated theo-
retically, and thus he succeeded in formulating certain
equations by which the problem of applying the quan-
tum theory has been solved in regard to its universal
validity. The close relation between this particular
method of reckoning and that of matrix computation
was brought to light by the collaboration of Max Born
and P. Jordan, and a further significant step in this di-
rection was accomplished by W. Pauli and P. Dirac.

It is remarkable how such a roundabout way, which
even sometimes appeared to run in opposite directions,
led to the selfsame goal and opened up new territory
which has extended the basis of the quantum theory.
A further extension followed, with the founding of the
wave-theory. The Heisenberg theory originally recog-
nized only integral magnitudes in the quantities meas-
ured. That is to say, his results verified the condition of
discontinuity postulated by the quantum theory. But
another and complementary interpretation developed

62 WHERE IS SCIENCE GOING?

independently of Heisenberg, out of suggestions first
made by L. de Broglie. The Einstein light quanta are
of a twofold nature. Looked at from the viewpoint of
energy, they act as discrete and invisible particles — that
is to say, they are concentrated quanta, or photons j but
if we consider them from the electromagnetic standpoint
all experiment has shown that they are like a spherical
wave or pulse spreading in all directions, completely
corresponding to the Maxwellian wave-theory of light.
This is one of the great dilemmas of modern physics.
And the hypothesis of wave-mechanics is an attempt to
solve it. It was E. Schroedinger who first presented an
exact analytical formulation of wave-mechanics, in the
partial differential equations adduced by him. For the
integral values of energy, on the one hand, this led
directly to the quantizing rules which Heisenberg had
laid down, while on the other hand it extended the
grounds of application of the quantum theory to dis-
integrating processes and even more tangled problems.
At the present stage of its development we can safely
say that the theory of wave-mechanics has definitely
established itself as a generalization and expansion of
the classical corpuscular mechanics. The difference be-
tween classical mechanics and wave-mechanics arises
principally from the circumstances that the laws of mo-
tion in respect of a physical picture cannot be formulated
as they were formulated in classical mechanics — that is
to say, the picture cannot be broken up into infinitesi-
mally small fractions and the movement of each fraction
dealt with independently of the others. On the contrary,

FIFTY YEARS OF SCIENCE 63

according to wave-mechanics, the picture must be held
before the eye as a whole and its movement must be
looked upon as arising from the individual and mutually
differentiated integral movements. From this it follows
closely that, not the local force — as in Newtonian
mechanics — but the integral force — that is to say, the
potential — enters the fundamental equations. Moreover
it follows that there can be no sense in talking about the
state of a particle in the sense of meaning its position and
velocity. This state at best is rather a certain underlying
space for the play of dimensional ordering of the quan-
tum of action. Therefore in principle every method of
measurement involves an uncertainty in regard to the
corresponding sum-total.

It goes without saying that the laws of nature are in
themselves independent of the properties of the instru-
ments with which they are measured. Therefore in every
observation of natural phenomena we must remember
the principle that the reliability of the measuring ap-
paratus must always play an important role. For this
reason many researchers in quantum physics are inclined
to set aside the principle of causation in the measurement
of natural processes and to adopt a statistical method in
its place. But instead of this I think it may be suggested
with equal justice that we might alter the formulation of
the causal principle as we have received it from classical
physics, so that it may again have its strict validity. But
this question as to the rival merits of the strictly causal
and statistical methods will depend upon how far the
one proves more fruitful of results than the other.

CHAPTER II
IS THE EXTERNAL WORLD REAL?

WE are living in a very singular moment of
history. It is a moment of crisis, in the literal
sense of that word. In every branch of our spiritual
and material civilization we seem to have arrived at
a critical turning-point. This spirit shows itself not
only in the actual state of public affairs but also in the
general attitude towards fundamental values in per-
sonal and social life.

Many people say that these symptoms mark the be-
ginnings of a great renaissance, but there are others
who see in them the tidings of a downfall to which
our civilization is fatally destined. Formerly it was
only religion, especially in its doctrinal and moral
systems, that was the object of skeptical attack. Then
the iconoclast began to shatter the ideals and principles
that had hitherto been accepted in the province of art.
Now he has invaded the temple of science. There is
scarcely a scientific axiom that is not nowadays denied
by somebody. And at the same time almost any non-
sensical theory that may be put forward in the name
of science would be almost sure to find believers and
disciples somewhere or other.

64

IS THE EXTERNAL WORLD REAL? 65

In the midst of this confusion it is natural to ask
whether there is any rock of truth left on which we can
take our stand and feel sure that it is unassailable and
that it will hold firm against the storm of skepticism
raging around it. Science, in general, presents us with
the spectacle of a marvelous theoretical structure which
is one of the proudest achievements of constructive
reasoning. The logical coherence of the scientific struc-
ture was hitherto the object of unstinted admiration on
the part of those who criticized the fundamentals of
art and religion. But this logical quality will not avail
us now against the skeptics' attack. Logic in its purest
form, which is mathematics, only coordinates and ar-
ticulates one truth with another. It gives harmony to
the superstructure of science ; but it cannot provide the
foundation or the building-stones.

Where shall we look for a firm foundation upon
which our outlook on nature and the world in general
can be scientifically based? The moment this question
is asked the mind turns immediately to the most exact
of our natural sciences, namely, Physics. But even
physical science has not escaped the contagion of this
critical moment of history. It is not merely that the
claim to reliability put forward by physical science is
questioned from the outside 5 but even within the
province of this science itself the spirit of confusion
and contradiction has begun to be active. And this
spirit is remarkably noticeable in regard to questions
that affect the very fundamental problem of how far
and in what way the human mind is capable of coming

66 WHERE IS SCIENCE GOING?

to a knowledge of external reality. To take one instance :
Hitherto the principle of causality was universally
accepted as an indispensable postulate of scientific re-
search, but now we are told by some physicists that
it must be thrown overboard. The fact that such an
extraordinary opinion should be expressed in respon-
sible scientific quarters is widely taken to be significant
of the all-round unreliability of human knowledge.
This indeed is a very serious situation, and for that
reason I feel, as a physicist, that I ought to put forward
my own views on the situation in which physical science
now finds itself. Perhaps what I shall have to say may
throw some light on other fields of human activity
which the cloud of skepticism has also darkened.

Let us get down to bedrock facts. The beginning
of every act of knowing, and therefore the starting-
point of every science, must be in our own personal
experiences. I am using the word, experience, here in
its technical philosophical connotation, namely, our
direct sensory perception of outside things. These are
the immediate data of the act of knowing. They form
the first and most real hook on which we fasten the
thought-chain of science 5 because the material that fur-
nishes, as it were, the building-stones of science is
received either directly through our own perception of
outer things or indirectly, through the information of
others, that is to say from former researchers and
teachers and publications and so on. There are no
other sources of scientific knowledge. In physical
science we have to deal specially and exclusively with

IS THE EXTERNAL WORLD REAL? 67

that material which is the result of observing natural
phenomena through the medium of our senses, with
of course the help of measuring instruments such as
telescopes, oscillators and so on. The reactions thus
registered in observing external nature are collated
and schematized on the basis of repeated observations
and calculations. This subject-matter of our scientific
constructions, being the immediate reactions of what
we see, hear, feel, and touch, forms immediate data
and indisputable reality. If physical science could dis-
charge its function by merely concatenating these data
and reporting them, then nobody could question the
reliability of its foundations.

But the problem is: Does this foundation fully meet
the needs of physical science? If we may say that it
is the business of physical science, solely and exclu-
sively, in the most accurate and most simple way, to
describe the order observed in studying various natural
phenomena, then is the task of physical science ade-
quately and exhaustively fulfilled? There is a certain
school of philosophers and physicists who hold that
this and this alone forms the scope of physical science.
Many outstanding physicists have been induced to ac-
cept this view because of the general confusion and
insecurity that arises from the skeptical spirit of the
times. They feel that here at any rate is a foundation
that is impregnable. The school which puts forward
this view is generally called the Positivist School $ and
in all that I have to say here I shall take the word
Positivism in that sense. Since the time of Auguste

68 WHERE IS SCIENCE GOING?

Comte, the founder of Positivism, many meanings
have been given to the word. Therefore I think it
well to declare here at the outset that I am restricting
its application to the definite meaning which I have
already indicated. This happens also to be the meaning
in which the word, Positivism, is most generally used.

Now let us ask, is the foundation which Positivism
offers broad enough to support the whole structure of
physical science? The best test that can be applied in
finding an answer to this question is to ask where Posi-
tivism would lead if we once were to accept it as
offering the sole groundwork of physical science.

Suppose for the moment that we are positivists.
And let us take the trouble to control ourselves so
that we shall hold strictly to its logical implications
and not allow commonplaces and considerations of
sentiment to lure us from the logical train of positivist
thought. Let us here and now decide that no matter
what singular consequences we may encounter in deal-
ing with the positivist line of thought we shall stick
steadfastly to it. And we shall be sure that in doing
so we cannot be faced with logical contradictions di-
rectly emerging from the field of observation -y because
obviously two actually observed facts in nature can-
not be in logical contradiction to one another. On the
other hand as long as we remain positivists we must
deal with every kind of experience and ignore no
source of human knowledge whatsoever. Therein lies
the strength of the positivist theory. As long as physi-
cal science sticks to the positivist rule it occupies itself

IS THE EXTERNAL WORLD REAL? 69

with all the problems that can be answered through
direct observation. Every problem that has a meaning
of definite importance comes within the ambit of
physical science under the positivist rule. If we are
to content ourselves with a direct observation of natu-
ral phenomena and the recording of them, we shall
obviously have no fundamental riddles to solve nor
any obscure questions. Everything will lie in the open
daylight. Thus far the state of affairs looks quite
simple. But it is no simple matter at all to carry out
the principle when we begin to deal with individual
cases. Our daily habits of speech make it rather diffi-
cult for us to observe the strict positivist rule. In ordi-
nary life when we speak of an outer object — a table,
for instance — we mean something that is different from
the table as actually observed by physical science. We
can see the table and we can touch it and we can try
its firmness by leaning on it and its hardness and if we
give it a thump with our knuckles we shall feel a hurt.
In the light of positivist science the table is nothing
more than a complex of these sensory perceptions and
we have merely got into the habit of associating them
with the word table. Remove these sensory perceptions
and absolutely nothing remains. In the positivist theory
we must entirely ignore everything beyond what is
registered by the senses and therefore we are impreg-
nable in this clearly defined realm. For the positivist,
to ask what a table in reality is has no meaning what-
soever -y and this is so with our other physical concepts.
The whole world around us is nothing but an analogue

70 WHERE IS SCIENCE GOING?

of experiences we have received. To speak of this world
as existing independently of these experiences is to
make a statement that has no meaning. If a problem
dealing with the external world does not admit of being
referred immediately to some kind of sensory experi-
ence and does not allow of being placed under observa-
tion, then it has no meaning and must be ruled out.
Therefore within the scope of the positivist system
there is no place for any kind of metaphysics. If we
glance upwards at the star-strewn firmament we see
innumerable points or patines of light which move in
a more or less regular way through the heavens. We
can measure the intensity and the color of their rays.
According to the positivist theory, these measurements
are not merely the raw material of astronomy and
astrophysics, but they are the sole and exclusive sub-
ject-matter of these sciences. Beyond merely recording
these measurements, astronomy and astrophysics have
nothing more to say. If they draw any inferences from
the measurements, these inferences cannot be con-
sidered as legitimate science. That is the positivist
standpoint. The mental constructions that we make in
collating and selecting and systematizing the measure-
ment data, and the theories which we advance to explain
why they should be so and not otherwise, are an un-
warranted human intrusion on the scene. They are
mere arbitrary inventions of human reason. They may
be convenient, just as the habit of thinking in similes
is a convenient help to the mind, but we have no right

IS THE EXTERNAL WORLD REAL? 71

to put them forward as representing anything that
really happens in nature.

All we know is the bare result of the sensory meas-
urements and we have no right to attach an ulterior
significance to these.

Supposing we say, with Ptolemy, that the earth is
the fixed center of the universe and that the sun and
all the stars move around it; or supposing we say,
with Copernicus, that the earth is a small particle of
matter which is relatively insignificant in relation to
the whole universe, turning on its axis once every
twenty-four hours and revolving around the sun once
in every twelve months — on the positivist principle
the one theory is as good as the other, when con-
sidered from the scientific viewpoint. They are merely
two different ways of making a mental construction
out of sensory reactions to some outer phenomena;
but they have no more right to be looked upon as
scientifically significant than the mental construction
which the mystic or poet may make out of his sensory
impressions when face to face with nature. It is true
that the Copernican theory of astronomy is more
widely accepted; but that is because it is a simpler
way of formulating a synthesis of sensory observations
and it does not give rise to so many difficulties about
astronomical laws as would arise from the acceptance
of the Ptolemaic theory. Therefore Copernicus is not
to be judged as a pioneer discoverer in the realms of
science, no more than a poet is to be judged as a
pioneer discoverer when he gives fanciful and attractive

72 WHERE IS SCIENCE GOING?

expression to sentiments that are known to every
human breast. Copernicus discovered nothing. He only
formulated, in the shape of a fanciful mental construc-
tion, a mass of facts that were already known. He did
not add anything to the store of scientific knowledge
already in existence. A tremendous mental revolution
was caused by his theory and bitter battles were waged
around it. For the logical consequence of it was to
give an entirely different account of man's place in
the universe from that generally held at the time by
the religion and philosophy of Europe. But for the
positivist scientist all the fuss and trouble made over
the Copernican theory were quite as senseless, from
the scientific point of view, as if one were to quarrel
with the rapture of a contemplative who gazes on the
Milky Way and ponders over the fact that each star
in that Milky Way is a sun somewhat like ours and
that each spiral nebula is again a Milky Way from
which the light has taken many millions of years to
reach our earth, while the earth itself, with its human
race on it, sinks away into an insignificant speck which
is hardly discernible in the boundless space.

Incidentally we must remind ourselves that to look
at nature in this way is to look at it from the aesthetic
and ethical standpoints. These, of course, have no
direct relation to physical science. Therefore they are
excluded. But in excluding them there is a fundamental
difference between the attitude of the non-positivist and
that of the positivist physicist. The ordinary scientist,
who does not believe in the positivist attitude, admits

IS THE EXTERNAL WORLD REAL? 73

the validity of the aesthetic standpoint and the ethical
standpoint j but he recognizes these as belonging to
another way of looking at nature. Such a way does not
come within the province of physical science. On the
other hand, the positivist does not admit any such
values as real at all, even in other provinces than
physical science. For him a beautiful sunset is merely
a sequence of sensory impressions. Therefore, as I
said at the beginning, as long as we logically pursue
the positivist teaching we must exclude every influence
of a sentimental, aesthetic or ethical character from
our minds. We have to keep to the logical track. That
is the indispensable guarantee of certainty which the
positivist teaching has to offer. And here I may remind
the reader once again that we are examining a system
which has been put forward with the very laudable
motive of furnishing a sure basis for the reliability of
science. Therefore the whole position must be dis-
cussed entirely objectively and free from any polemical
feeling.

In the positivist way of looking at nature sensory
impressions are the primary data and therefore signify
immediate reality. From this it follows that in principle
it would be a mistake to speak of the senses themselves
being deceived. What under certain circumstances can
be deceptive are not the sensory impressions themselves
but the conclusions we so often draw from them. If
we plunge a straight stick into water and hold it slant-
wise, and notice the apparent bend at the point of im-
mersion, we are not deceived by the sense of sight into

74 WHERE IS SCIENCE GOING?

thinking that the stick is thereby bent. There is an
actual bending present as an optical perception ; but
that is quite a different thing from concluding that the
stick itself is bent. The positivist will not allow us to
conclude anything. We have a sensory impression of
the part of the stick that is in water and a contiguous
sensory impression of the part that is in air; but we
have no right to say anything about the stick itself.
The most that the positivist principle will allow us
to say is that the stick looks "as if" it were bent. If
we explain the whole phenomenon by saying that the
light rays which are reflected in the air from the stick
to the eye pass through a less dense medium than that
through which the rays pass when reflected from the
part of the stick immersed in water, and that therefore
the latter are more strongly deflected, that way of
stating the case is useful from many points of view
but it is no closer to reality than to say that the senses
perceive the stick "as if" it were bent.

The essential point here is that, from the standpoint
of Positivism, both ways of stating the case are funda-
mentally of equal validity. And there would be no
sense in attempting to judge their rival validities by
asking how far one is more appropriate than the other,
by appealing to the sense of touch to rectify the ap-
parent anomaly of a stick which was straight in air
being bent in water. In the positivist system there would
be no meaning in a decision one way or another; be-
cause a strictly logical positivist science would have to
be content with merely noting the sensory impressions

IS THE EXTERNAL WORLD REAL? 75

and leaving the matter at that. We could say that the
stick looks "as if" it were bent. In practice, of course,
anything like a serious attempt at an all-round appli-
cation of this "as if" theory would lead to ridiculous
consequences. But here we are not testing the positivist
theory by any such grounds. We are considering it on
its own chosen ground of logical consistency, which is
its bedrock foundation. It must stand or fall by the
consequences that would result for physical science by
the logical application of the positivist premises.

What I have said here in regard to the stick applies
equally to all the surrounding objects of inanimate
nature. In the positivist view a tree is nothing more
than a complex of sense-impressions. We can see it
grow. We can hear the rustle of its leaves and inhale
the perfumes of its blossoms. But if we take away all
these sensory impressions then nothing remains to cor-
respond to what may be called the "tree in itself."

What holds good for the world of plant life must
also have meaning for the animal world. We speak
of this world as a special and independent realm of
being, but that is solely because it is a convenient way
of thinking and talking. If we tread on a worm it
squirms. That we can see. But there would be no sense
in asking if the worm suffers pain thereby. For a man
can feel only his own pain and he cannot with any
certainty of knowledge extend that same feeling to
the animal world. To say that an animal suffers pain
is an assumption based on a summary of various char-
acteristics that correspond to what happens in our own

76 WHERE IS SCIENCE GOING?

case under similar circumstances. In the case of a worm
we notice a squirming or shrugging. In the case of
other animals we notice contortions of the face and
body. These are analogous to what happens in our case
under like conditions. And there are certain cries in
I the animal world which are analogous to the sounds
we utter when we suffer pain.

When we come from the animal world to the world
of human beings we find the positivist scientists making
a clear distinction between one's own impressions and
the impressions of others. One's own impressions are
the sole reality and they are realities only for oneself.
The impressions of another person are only indirectly
knowable to us. As objects of knowledge they signify
something fundamentally different from our own im-
pressions. Therefore in speaking of them we are merely
following the same sort of useful analogy as when we
speak of the suffering of animals. But, in the strict
positivist view, we have no reliable knowledge what-
soever of other people's impressions. Because they are
not a direct sensory perception, they do not furnish a
basis for the certainty of our knowledge.

It is quite clear that the positivist outlook cannot
be accused of logical inconsistency. So long as we stick
closely to its principles we do not find ourselves up
against any contradiction. That is the strong point of
the whole system. But when we come to apply it as
the exclusive foundation on which scientific research
can be carried on we shall find that the result would
be of very significant import for physical science. If

IS THE EXTERNAL WORLD REAL? 77

the scope of physical science extends no further than
the mere description of sensory experiences, then strictly
only one's own experiences can be taken as the object
of such description 5 because only one's own experiences
are primary data. Now it is clear that on the basis of
a mere individual complex of experience not even the
most gifted of men could construct anything like a
comprehensive scientific system. So we are faced with
the alternative of either renouncing the idea of a com-
prehensive science, which will hardly be agreed to even
by the most extreme positivist, or to admit a compro-
mise and allow the experiences of others to enter into
the groundwork of scientific knowledge. But we should
thereby, strictly speaking, give up our original stand-
point, namely, that only primary data constituted a
reliable basis of scientific truth. The sensory impressions
of others are secondary and they are data for us only
through the reports we have of them. This brings a
new factor into play here, namely, the trustworthiness
of oral and written information in scientific reports.
Therewith we break at least one link of the logical
chain which holds the positivist system together ; for the
foundational principle of the system is that only imme-
diate perception can be considered as offering material
for scientific certainty.

Let us, however, pass over this difficulty and let us
assume that all reports furnished by scientific research-
ers are reliable or at least that we have an infallible
means of excluding those which are unreliable. In this
case it is obvious that the reports furnished by the

78 WHERE IS SCIENCE GOING?

numerous scientists who were and are acknowledged as
honorable and reliable both in the past and to-day must
be taken into scientific consideration j and there are no
grounds whereon some should be excluded in favor of
others. It would be quite wrong to devaluate the claims
of any investigators on the grounds that his findings
have not been corroborated by others.

If we should stick to this idea then it would be diffi-
cult to explain or to justify the conduct of physical
science in regard to certain individual researchers. Let
us take one instance as illustrative.

The so-called N-rays which were discovered by the
French physicist, Blondlot, in the year 1903, and at
that time studied on all sides, are to-day entirely
ignored. Rene Blondlot, who was professor at the Uni-
versity of Nancy, was admittedly an excellent and
reliable investigator. His discovery was for him an ex-
perience as great as that of any other physicist. We
cannot say that he was fooled by his sense-perceptions $
for in positivist physics, as we have seen, there is no
such thing as delusion in sensuous perception. It would
be only proper and right to look upon the N-rays as
primary reality-data, something that directly struck the
perception of one man. And if since the time of Blond-
lot and his school no man throughout all the years
between has succeeded in reproducing them, that is no
reason for saying — at least from the positivist stand-
point— that they will not one day, under some special
circumstances, yet again become discernible.

Under the positivist test we should have to agree

IS THE EXTERNAL WORLD REAL? 79

that the number of those researchers whose findings are
of value for physical science is indeed very small. We
should have to admit only those who devote themselves
specially to this science, because the discoveries which
outsiders have made in this field are more or less
insignificant. Moreover, we must from the outset ex-
clude all theoretical physicists j for their experiences
are restricted essentially to the use of pen, ink, and
paper and abstract reasoning. And thus we have only
the experimental physicists remaining, and in the first
line only those who confine themselves to the operation
of extremely sensitive instruments for special investi-
gation. Therefore in the positivist hypothesis only a
small roll of specially qualified physicists come into
the picture when we speak of the contributions of
those who have devoted themselves to the progress of
physical science.

From this standpoint how are we to explain the
extraordinary impression made and the revolution
which was created in the world of international science
by the findings, for instance, of Oersted, who detected
the influence of a galvanic current on the compass
needle, or of Faraday, who first discovered the effect
of electromagnetic induction, or of Hertz, who discov-
ered small electric sparks in the focus of his parabolic
reflector by the use of the magnifying glass? How and
why did these individual sensory impressions create
such a furore and lead to such a world revolution in
the theory and application of scientific methods? To
this question the upholders of positivism can give only

8o WHERE IS SCIENCE GOING?

a roundabout and entirely unsatisfactory answer. They
have to fall back upon the theory that these individual
experiences, which were insignificant in themselves,
merely opened up a viewpoint as a result of which
other researchers were led to the discovery of a series
of much greater and more portentous results. That is
a rather lame answer but it illustrates very well the
positivist position, because the upholder of positivism
will admit nothing except a bald description of results
experienced in research ; and if we ask why it is that
certain findings of a few obscure individuals, carried
out under quite primitive conditions, had such an im-
mediate and world-wide significance for all other
physicists — that question has no meaning for physical
science as viewed from the positivist standpoint.

The reason for taking up this striking attitude is
quite easy to understand. Those who lean towards the
discipline that I have been describing deny the idea
and the necessity of an objective physical science which
is independent of the actually experiencing and sense-
perceiving investigator. They cling to this attitude be-
cause they are bound logically to acknowledge no other
i reality save that of the factual experience of the indi-
vidual physicist. Now I think it is obvious here that
if physical science as such were to accept this position,
as the exclusive basis of its research, then it would find
itself trying to support a huge structure on a very
inadequate foundation. A science that starts off by pre-
dicting the denial of objectivjty has already passed
sentence on itself. Of what value to the world are

IS THE EXTERNAL WORLD REAL? 81

the sensory impressions of a mere individual? Yet that
is the foundation to which in the last analysis physical
science is reduced in looking for a basis for its struc-
ture. This plot is entirely too small for such a building.
It has to be extended by the addition of other ground.
No science can rest its foundation on the dependability
of single human individuals. And the moment we have
made that statement we have taken a step which puts
us off the logical pathway of the positivist system. We
have followed the call of common sense. We have taken
a jump into the metaphysical realm ; because we have
accepted the hypothesis that sensory perceptions do not
of themselves create the physical world around us, but
rather that they bring news of another world which
lies outside of ours and is entirely independent of us.

And thus we strike out the positivist als-ob (As-If) j
and attribute a higher kind of reality than that of mere
description of immediate sensory impressions to the
practical discoveries that have been already mentioned
— Faraday's, etc. Once we take this step we lift the
goal of physical science to a higher level. It is not
restricted to the mere description of bare facts of ex-
perimental discovery j but it aims at furnishing an
ever increasing knowledge of the real outer world
around us.

At this point a new epistemological 1 difficulty enters.
The basic principle of the positivist theory is that there
is no other source of knowledge except within the re-
stricted range of perception through the senses. Now

1 Epistemology is the Science of the Nature of Knowledge.

82 WHERE IS SCIENCE GOING?

there are two theorems that form together the cardinal
hinge on which the whole structure of physical science
turns. These theorems are: (i) There is a real outer
world which exists independently of our act of know-
ing) and, (2) The real outer world is not directly know-
able. To a certain degree these two statements are
mutually contradictory. And this fact discloses the
presence of an irrational or mystic element which ad-
heres to physical science as to every other branch of
human knowledge. The knowable realities of nature
cannot be exhaustively discovered by any branch of
science. This means that science is never in a position
completely and exhaustively to explain the problems it
has to face. We see in all modern scientific advances
that the solution of one problem only unveils the mys-
tery of another. Each hilltop that we reach discloses
to us another hilltop beyond. We must accept this as
a hard and fast irrefutable fact. And we cannot remove
this fact by trying to fall back upon a basis which would
restrict the scope of science from the very start merely
to the description of sensory experiences. The aim of
science is something more. It is an incessant struggle
towards a goal which can never be reached. Because
the goal is of its very nature unattainable. It is some-
thing that is essentially metaphysical and as such is
always again and again beyond each achievement.

But if physical science is never to come to an ex-
haustive knowledge of its object, then does not this
seem like reducing all science to a meaningless activity?
Not at all. For it is just this striving forward that

IS THE EXTERNAL WORLD REAL? 83

brings us to the fruits which are always falling into
our hands and which are the unfailing sign that we
are on the right road and that we are ever and ever
drawing nearer to our journey's end. But that journey's
end will never be reached, because it is always the still
far thing that glimmers in the distance and is unattain-
able. It is not the possession of truth, but the success
which attends the seeking after it, that enriches the
seeker and brings happiness to him. This is an acknowl-
edgment made long ago by thinkers of deepest insight,
even before Lessing gave it the classic stamp of his
famous phrase.

CHAPTER III

THE SCIENTIST'S PICTURE OF THE
PHYSICAL UNIVERSE

THE ideal aim before the mind of the physicist is
to understand the external world of reality. But
the means which he uses to attain this end are what are
known in physical science as measurements, and these
give no direct information about external reality. They
are only a register or representation of reactions to
physical phenomena. As such they contain no explicit
information and have to be interpreted. As Helmholtz
said, measurements furnish the physicist with a sign
which he must interpret, just as a language expert in-
terprets the text of some prehistorical document that be-
longs to a culture utterly unknown. The first thing which
the language expert assumes — and must assume if his
work is to have any practical meaning — is that the docu-
ment in question contains some reasonable message
which has been stated according to some system of
grammatical rules or symbols. In the same way the
physicist must assume that the physical universe is gov-
erned by some system of laws which can be understood,
even though he cannot hold out to himself the prospect
of being able to understand them in a comprehensive

84

NATURE'S IMAGE IN SCIENCE 85

way or to discover their character and manner of opera-
tion with anything like a full degree of certitude.

Taking it, then, that the external world of reality
is governed by a system of laws, the physicist now con-
structs a synthesis of concepts and theorems 5 and this
synthesis is called the scientific picture of the physical
universe. It is a representation of the real world itself
in so far as it corresponds as closely as possible to the
information which the research measurements have sup-
plied. Once he has accomplished this the researcher can
assert, without having to fear the contradiction of facts,
that he has discovered one side of the outer world of
reality, though of course he can never logically demon-
strate the truth of the assertion.

If we consider the efforts that have been made by
physicists, ever since the days of Aristotle, to describe
the external universe, I think we need have no hesita-
tion in expressing unqualified admiration for the ex-
traordinary degree of perfection achieved in this re-
spect by the inventive mind of the scientific researcher.
From the positivist standpoint, of course, this idea of
constructing a scientific picture of the physical universe
— this continual striving after a knowledge of external
reality — is something foreign and meaningless. For
where there is no outer object there is nothing that can
be portrayed or described.

The chief quality to be looked for in the physicist's
world-picture must be the closest possible accord be-
tween the real world and the world of sensory experi-
ence. What is taken in through the senses is the first

86 WHERE IS SCIENCE GOING?

material that the physicist has to work upon. And the
first process which this raw material must undergo is
one of elimination and refinement. From the whole
complex of sensory data everything must be cut away
and discarded which may have arisen from the sub-
jective constructive tendencies of the sensory organs
themselves. And, furthermore, everything must be
eliminated which can be attributed to the accident of
special circumstances. In this latter connection attention
must be paid to the fact that measuring instruments
may affect the results that are being arrived at during
the process of observation. That is all the more likely
to be the case in the observation of minutiae.

Supposing all the above conditions to have been
verified, then the physicist's picture of the external
universe has only one further requirement to fulfill.
Throughout its whole composition it must be free from
everything in the nature of a logical incoherence. Other-
wise the researcher has an entirely free hand. He may
give rein to his own spirit of initiative and allow the
constructive powers of the imagination to come into
play without let or hindrance. This naturally means that
he has a significant measure of freedom in making his
mental constructions ; but it must be remembered that
this freedom is only for the sake of a specific purpose
and is a constructive application of the imaginative
powers. It is not a mere arbitrary flight into the realms
of fancy.

The physicist is bound, by the very nature of the
task in hand, to use his imaginative faculties at the very

NATURE'S IMAGE IN SCIENCE 87

first step he takes. For the first stage of his work must
be to take the results furnished by a series of experi-
mental measurements and try to organize these under
one law. That is to say, he must select according to a
plan which will in the first instance be hypothetical and
therefore a construction of the imagination. And when
he finds that the given results will not fit into one plan
he discards it and tries another. This means that his
imaginative powers must always be speculating on the
significance of the data which have been furnished
through experimental measurements. He is in the same
position as a mathematician who is presented with a
number of single points that have to be joined together
with a curve. The closer together and the more
numerous these points are, the more innumerable will
be the possible kinds of alternative curves that present
themselves to the mind. We meet with practically the
same task when we follow the movements of a sensitive
registering instrument which is designed to mark only
one independent and definite curve, such as the tem-
perature curve y for we find that this curve is never
sharply defined but is always a more or less broad stroke
in which an endless number of sharp curves find their
place.

As to how one may reach a decision in the midst of
this uncertainty, no general rule of procedure can be
laid down. One must simply choose a definite line of
thought. And that line of thought ought to be directed
towards founding, on the basis of a selected combination
of ideas, a hypothesis in the light of which we can out-

88 WHERE IS SCIENCE GOING?

line the curve we are seeking for, and outline it in such
a way that it will have a clarity and definiteness of its
own that distinguishes it from the numberless other
curves intruding on the scene. In other words, where
the spectrum shows for instance a diversified picture,
and where we are seeking for the cause of only one
element in that picture, we have to imagine a number of
hypothetical causes and examine them one after the
other until we hit upon something that will accord with
a certain series of results that are pictured on the spec-
trum. The line of thought which leads to these various
alternatives has its origin entirely outside the ambit of
logic. In order to formulate this kind of hypothesis the
physicist must possess two characteristics. He must have
a practical knowledge of his whole field of work and
he must have a constructive imagination. This means
that, in the first place, he must be acquainted with other
kinds of measurements besides the one that he is actually
using. And, in the second place, he must have the knack
of combining under one viewpoint the results obtained
through two different kinds of measurement.

Every hypothesis that is productive of results has its
origin in some fortunate juxtaposition of two different
ways in which observations have presented themselves.
We see this truth very clearly illustrated in the famous
historical cases that have led to epoch-making dis-
coveries.

When Archimedes had noted the loss of weight
registered by his own body in water he connected this
fact with the loss of weight which various other bodies

NATURE'S IMAGE IN SCIENCE 89

would undergo on being placed in water, and thus he
arrived at a means of finding out the specific gravities
of various metals. This came into his head one day while
in his bath and meditating how he could assay the golden
crown of the King of Syracuse, which was suspected
of containing a silver alloy, though it purported to be of
pure gold. Applying the experience of his own loss of
weight in the bath, it struck him that the excessive bulk
occasioned by the alloy could be detected by putting the
crown, and equal weights of gold and silver, separately
in a vessel of water and measuring the difference of the
overflow. Newton noticed the movement of an apple
falling from a tree in his orchard and he connected that
observation with the motion of the moon in relation to
the earth. Einstein observed the state of a gravitating
body in a fixed box, and considered this in juxtaposition
with the state of a body free from gravitation in a box
subjected to a process of upward acceleration. Niels
Bohr associated the orbital rotation of the electrons
around the nucleus of an atom with the movement of
planets around the sun. All these combinations were
productive of famous results. Indeed it would be an
interesting mental exercise if one were to take as many
as possible of the hypotheses which have proved sig-
nificant of results in the pursuit of physical science and
then try to discover the respective combinations of ideas
to which the hypotheses owed their origin. But the task
would be a difficult one because, generally speaking,
creative master minds have felt a personal aversion
to the idea of unfolding before the public gaze those

90 WHERE IS SCIENCE GOING?

delicate threads of thought out of which their produc-
tive hypotheses were woven, and the myriad other
threads which failed to be interwoven into any final
pattern.

The utility of an hypothesis, once it has been put
forward, can be tested only by following out the logical
results that flow from its application. This has to be
done in a purely logical — and primarily mathematical
— way, whereby the hypothesis is used as a starting-
point and as complete a theoretical system as possible is
developed from it. Once the theoretical system has thus
been fully developed it will be put to the test of the
measurements which have been furnished by factual
experiment. According as the system closely corresponds
with these measurements we can judge whether the
hypothesis from which we started was or was not suc-
cessfully chosen.

Such being the actual method of procedure adopted
by the physicist, we can understand at once how it is
that the progress of physical science does not follow
a regular curve of development, which might mark an
all-round process of increasing depth and precision in
the knowledge we are gaining of the external world.
It is rather a zigzag pattern that the curve of scientific
progress follows ; indeed I might say that the forward
movement is of an explosive type, where the rebound
is an attendant characteristic of the advance. Every
applied hypothesis which succeeds in throwing the
searchlight of a new vision across the field of physical
science represents a plunge into the darkness ; because

NATURE'S IMAGE IN SCIENCE 91

we cannot at first reduce the vision to a logical state-
ment. Then follows the birth-struggle of a new theory.
Once this has seen the light of day it has to go forward
willy-nilly until the stamp of its destiny is put on it
when the test of the research measurements is applied.
If the hypothesis survives this test, then it advances in
prestige and acceptance and the theory arising from its
application develops and expands to a more and more
comprehensive ambit.

But, on the other hand, if the application of research
measurements places difficulties to the viability of our
hypothesis, then fears and misgivings and critical birth
conditions set in. But these are the signs of the breaking
up of old acceptances and the bringing to birth of a new
hypothesis. The task of the latter will be to push for-
ward to the solution of the crisis out of which it was
born, and to construct a new theory which will preserve
what was genuine in the old order of things, while cor-
recting and discarding the mistakes. So, in the everlast-
ing interplay of change succeeding upon change, the
knowledge which physical science brings to us comes at
one time with hesitating step and at another with a for-
ward bound, in its way towards the discovery of the real
external universe.

This has been a regularly recurrent feature through-
out the historical development of physical science. Take
the case of the Lorentzian theory of electrodynamic
motion. The conflicts and contradictions which were set
afoot by the application of actual research measure-
ments in this case are well known , but only those who

92 WHERE IS SCIENCE GOING?

have closely followed the thorny path of the Lorentzian
theory step by step can rightly appraise the relief which
came to hand when the Relativity hypothesis was first
established. An almost exactly similar experience has
been encountered in the history of the quantum theory ;
but in this latter case the crisis is not yet entirely passed.

It has already been said that in the statement of any
hypothesis the author of it has a free hand from the
very start. He has full and free choice of the concepts
and theorems which he will employ in framing his
synthesis, provided, of course, that there is no logical con-
tradiction between them. It is not true, as has often been
stated in physicist circles, that in the exposition of an
hypothesis the explorer must draw the material for his
ideas solely and strictly from those original data which
have been definitely furnished by the results of the re-
search measurements. This would mean that the forma-
tive concepts which give shape to an hypothesis must be
strictly independent of all theoretical origin. That is not
so. For, on the one hand, every hypothesis — as a factor
in the picture of the external universe presented by the
physicist — is a product of the freely speculating human
mind; and, on the other hand, there are no physical
formulae whatsoever which are the immediate results of
research measurements. The opposite is the case. Every
measurement first acquires its meaning for physical sci-
ence through the significance which a theory gives it.
Anybody who is familiar with a precision laboratory will
agree that even the finest and most direct measurements
— such as those of weight and current — have to be cor-

NATURE'S IMAGE IN SCIENCE 93

rected again and again before they can be employed
for any practical purpose. It is obvious that these cor-
rections cannot be suggested by the measurement process
itself. They must first be discovered through the light
which some theory or other throws upon the situation j
that is to say, they must arise from an hypothesis.

The truth of the whole matter is that the inventor of
an hypothesis has unlimited scope in the choice of what-
ever means he may deem helpful to his ultimate pur-
pose. He is not hindered by the physiological tendencies
towards constructive picturing which are a feature of
the activity of his own sense-organs. Nor is he restricted
by the guiding hand of his physical measuring-gear.
With the eye of the spirit he penetrates and supervises
the most delicate processes that unfold themselves in the
pattern of the physical universe which unrolls before
him. He follows the movements of every electron and
watches the frequency and form of every wave. He
even invents his own geometry as he goes along. And so
with his spiritual working-gear, with these instruments
of ideal exactitude, he takes a personal part, as it were,
in every physical process that happens before him. And
all this is for the purpose of pushing through these dif-
ficult thought experiments — which are a factor of every
research process — to the final establishment of conclu-
sions that will be of wide application. Naturally all such
conclusions have, at the outset of their statement, noth-
ing to do with the real research measurements. And
therefore an hypothesis can never be declared true or
false in the light of such measurements. All that can be

94 WHERE IS SCIENCE GOING?

asked about it is how far it reaches or falls short of serv-
ing some practical purpose or other.

And now we come to the other side of the picture.
This ideal clear-sightedness of the spiritual eye, in see-
ing behind the various processes of physical nature, is
due exclusively to the fact that the nature of the physi-
cal world in this case is something that is fashioned by
the mind of the observer himself. As long as this world
of his intuitive construction remains a hypothetical
world, the creator has full knowledge of it, and full
dominion over it and can shape it what way he will;
because as far as concerns reality it has as yet no value.
The first value comes the moment the theoretical system
on which this hypothetical world has been planned is
brought into touch with actual results that have been
furnished through research measurements.

Now, a merely physical measuring process tells us
just as little about the account which we are to give of
the physical universe as it does about the reality of that
universe itself. Indeed the process of research measure-
ment rather represents a happening in the sense-organs
of the researcher in relation to the happening that takes
place in the apparatus that he is using. All that can be
definitely said about this relation in respect of outer
reality is that there is some connection or other between
them. The measurement itself gives no immediate re-
sults that have a meaning of their own. And it is
the task of science to try to establish the meaning of the
above-mentioned connection, quite as much as it is the
task of the scientific explorer to carry out the actual

NATURE'S IMAGE IN SCIENCE 95

physical measurements themselves. The former task can
be accomplished only by the speculative mind of the
researcher.

The epistemological difficulties which have arisen in
the sphere of theoretical physics through the develop-
ment of the quantum theory seem to be due to the fact
that the bodily eye of the measuring physicist has been
identified with the spiritual eye of the speculative scien-
tist. As a matter of fact, the bodily eye, being part of
the physical process of nature itself, is the object rather
than the subject of scientific exploration. For as every
act of research measurement has a more or less causal
influence on the very process that is under observation,
it is practically impossible to separate the law that we
are seeking to discover behind the happening itself from
the methods that are being used to bring about the dis-
covery.

It is true that where there is question of natural
phenomena in the lump, such as a group of atoms taken
together, the method of measurement is not so likely
to influence the course of the events observed. And it is
for this reason that in the earlier stages of physical
science, which are now called the classical physics, the
opinion held sway that the actual measurement itself
furnishes a direct glimpse into the real happenings of
nature. But in this assumption, as we have already seen,
there was a fundamental mistake which is the counter-
part of the positivist error, namely, the paying of atten-
tion solely to the results given by experimental measure-
ments and entirely ignoring the inner reality of natural

96 WHERE IS SCIENCE GOING?

processes. Yet while we recognize this as a mistake on
the one side we must also realize on the other side that
if we are to abandon the measuring method we have
no way of coming into touch with the real happenings
themselves. But when we are faced with the indivisible
quantum of action, the limit is laid with mathematical
accuracy, beyond which the most delicate physical meas-
urement is unable to give a satisfactory answer to ques-
tions connected with the individual behavior of the more
minute processes. The result is that the problem of these
infinitesimal processes has no longer a meaning for
purely physical research. Here we come to the point
where such problems have to be dealt with by the specu-
lative reason. And it is in this abstract way that they
must be taken into account in our attempt to complete
the physicist's picture of the universe and thus bring us
nearer to the discovery of external reality itself.

Taking a glance backwards over the road along which
physical science has hitherto advanced we must admit
that further progress will depend essentially on the de-
velopment and wider application of our methods of
measurement. Thus far I am at one with the positivist
outlook. But the difference between us is that positivism
holds research measurement, through sensory percep-
tion, as the be-all and end-all of the processes through
which physical science advances, whereas I hold that the
study of physical realities treats measurement results as
a more or less intricate complex representing the regis-
tration of reactions to happenings in the external world,
the accuracy of which registration is relatively depend-

NATURE'S IMAGE IN SCIENCE 97

ent on what takes place in the registering instruments
themselves and in the interpretative sensory organs of
the researcher. The adequate analysis and correction
of this complex report is one of the chief functions of
scientific research. Therefore from the results that are
given by experimental measurements we must choose
those which will have a practical bearing on the object
of our inquiry, because each particular attempt at dis-
covering reality in the physical universe represents a
special form of a certain question which we put to
nature.

Now you cannot put a reasonable question unless you
have a reasonable theory in the light of which it is
asked. In other words, one must have some sort of
theoretical hypothesis in one's mind and one must put
it to the test of research measurements. This is why it
often happens that a certain line of research has a mean-
ing in the light of one theory but not in that of another.
And very often the significance of a question changes
when the theory in the light of which it is asked has
already changed.

Let us take for example the transmutation of some
common metal, such as quicksilver, into gold. For those
who lived in the days of alchemists this problem had a
very important significance and innumerable researchers
sacrificed their means and their life's efforts in an at-
tempt to solve it. The problem lost all its meaning, and
came to be looked upon as a fool's pursuit, when the
dogma of the intransmutability of atoms was introduced.
But now once again, since Bohr has put forward his

98 WHERE IS SCIENCE GOING?

theory that the gold atom is different from the quick-
silver atom only by the lack of one single electron, the
problem has become so vital that it is being newly
worked upon with the use of the most modern research
methods. Here again one sees the truth of the old adage,
that experience is the pathfinder of scientific study.
When intelligently worked out, even the most useless
experiments may result in opening up a way to the most
important discoveries.

It was thus that those more or less planless attempts
to make gold opened up the way to the introduction of
scientific chemistry. So too from the unsolved problem
of the perpetuum mobile finally arose the principle of
the conservation of energy. And the long series of vain
attempts to measure the movement of the earth led at
last to the suggestion of the conditions from which the
theory of relativity arose. Experimental and theoretical
adventures in science are always interdependent. The
one cannot progress without the other.

It often happens that when a new advance in theo-
retical science has definitely established itself certain
problems connected with it are branded as meaningless.
Not only that, but attempts are also sometimes made to
prove such problems meaningless on a friori grounds.
That is a delusion. In itself neither the absolute motion
of the earth — that is to say, the motion of the earth
in relation to the light-ether — nor the absolute New-
tonian space, is meaningless, as has often been declared
by popular exponents of the relativity theory. The
former problem is meaningless only when you intro-

NATURE'S IMAGE IN SCIENCE 99

duce the special theory of relativity, and the latter is
meaningless only when you introduce the general rela-
tivity theory.

So when we look back over the centuries we see that
doctrines on the interpretation of nature, which were
held as sound and good for their time, fell from honor
when faced with the light of some new scientific theory.
They served their day and then they passed. And
though succeeded by more scientifically enlightened
dogmas we must remember that those old theories had
sense and meaning for their age, as other theories will
have had sense and meaning for our time ; until another
day comes when newer theories will arise to take their
place.

The Law of Causality was unanimously accepted until
recent times as a fundamental principle in scientific re-
search. But now a battle of opinions is being waged
around it. Does the principle of causality, as hitherto be-
lieved, hold good in all its force for every physical hap-
pening? Or has it only a summary and statistical signifi-
cance when applied to the finer atoms? This question
cannot be decided by referring it to any epistemological
theory or by putting it to the test of research measure-
ments. In his attempt to build up his hypothetical pic-
ture of the external universe the physicist may or may
not, just as he likes, base his synthesis on the principle of
a strict dynamic causality or he may adopt only a statisti-
cal causality. The important question is how far he gets
with the one or the other. And that can be answered
only by choosing provisionally one of the two stand-

100

WHERE IS SCIENCE GOING?

points and studying the conclusions which can be logi-
cally derived from the adoption of that standpoint,
just as we did when dealing with Positivism.

In principle it does not matter which of the two stand-
points is chosen first. In practice one will naturally
choose that which promises to turn out more satisfactory
in its logical results. And here I must definitely declare
my own belief that the assumption of a strict dynamic
causality is to be preferred, simply because the idea of
a dynamically law-governed universe is of wider and
deeper application than the merely statistical idea,
which starts off by restricting the range of discovery 5
because in statistical physics there are only such laws as
refer to groups of events. The single events, as such, are
introduced and recognized expressly 5 but the question
of their law-governed sequence is declared senseless on
a fr'tori grounds. That way of procedure appears to me
to be highly unsatisfactory. And I have not been able to
find the slightest reason, up to now, which would force

us to give up the assumption of a strictly law-governed
universe, whether it is a matter of trying to discover the
nature of the physical, or the spiritual, forces around us.

It is obvious, of course, that no strictly causal connec-
tion can be deduced from a succession of experimental
experiences. Between these experiences as they succeed
one another we can establish only a statistical relation.
Even the acutest measurements are subject to accidental
and uncontrollable mistakes.

An experimental observation presents, as we have
seen, a complex result made up of several different ele-

NATURE'S IMAGE IN SCIENCE 101

ments. And even though each element were the direct
causal consequence of one other single element, yet we
cannot treat this original element as strictly causal in the
experiment, independently of the others j because diver-
sified results may follow from the combination in which
each elemental factor is applied.

And here a question arises which seems to set a defi-
nite impassable limit to the principle of strict causality,
at least in the spiritual sphere. This question is of such 1,
urgent human interest that I think it will be well if I
treat it here before I come to a close. It is the question
of the freedom of the human will. Our own conscious-
ness tells us that our wills are free. And the information
which that consciousness directly gives us is the last and
highest exercise of our powers of understanding.

Let us ask for a moment whether the human will is
free or whether it is determined in a strictly causal way.
These two alternatives seem definitely to exclude one
another. And as the former has obviously to be answered
in the affirmative, so the assumption of a law of strict
causality operating in the universe seems to be reduced
to an absurdity in at least this one instance. In other
words, if we assume the law of strict dynamic causality *
as existing throughout the universe, how can we logi-
cally exclude the human will from its operation?

Many are the attempts that have been made to solve
this dilemma. The purpose which in most cases they
have to set themselves has been to establish an exact
limit beyond which the law of causality does not apply.
Recent developments in physical science have come into

102 WHERE IS SCIENCE GOING?

play here, and the freedom of the human will has been
put forward as offering logical grounds for the accept-
ance of only a statistical causality operative in the physi-
cal universe. As I have already stated on other occasions,
I do not at all agree with this attitude. If we should
accept it, then the logical result would be to reduce the
human will to an organ which would be subject to the
sway of mere blind chance. In my opinion the question
. of the human will has nothing whatsoever to do with
the opposition between causal and statistical physics. Its
importance is of a much more profound character and is
entirely independent of any physical or biological
hypothesis.

I am inclined to believe, with many famous philoso-
phers, that the solution of the problem lies in quite an-
other sphere. On close examination, the above-stated
alternative — Is the human will free or is it determined
by a law of strict causality? — is based on an inadmis-
sible logical disjunction. The two cases opposed here are
not exclusive of one another. What then does it mean
if we say that the human will is causally determined?
It can only have one meaning, which is that every single
act of the will, with all its motives, can be foreseen and
predicted, naturally only by somebody who knows the
human being in question, with all his spiritual and physi-
cal characteristics, and who sees directly and clearly
through his conscious and subconscious life. But this
would mean that such a person would be endowed with
absolutely clear-seeing spiritual powers of vision; in
other words he would be endowed with divine vision.

NATURE'S IMAGE IN SCIENCE 103

Now, in the sight of God all men are equal. Even the
most highly gifted geniuses, such as a Goethe or a
Mozart, are but as primitive beings the thread of whose
innermost thought and most finely spun feelings is like
a chain of pearls unrolling in regular succession before
His eye. This does not belittle the greatness of great
men. But it would be a piece of stupid sacrilege on our
part if we were to arrogate to ourselves the power of
being able, on the basis of our own studies, to see as
clearly as the eye of God sees and to understand as
clearly as the Divine Spirit understands.

The profound depths of thought cannot be pene-
trated by the ordinary intellect. And when we say that
spiritual happenings are determined, the statement
eludes the possibility of proof. It is of a metaphysical
character, just as the statement that there exists an
outer world of reality. But the statement that spiritual
happenings are determined is logically unassailable, and
it plays a very important role in our pursuit of knowl-
edge, because it forms the basis of every attempt to
understand the connections between spiritual events. No
biographer will attempt to solve the question of the mo-
tives that govern the acts of his hero by attributing these
to mere chance. He will rather attribute his inability to
the lack of source materials or he will admit that his own
powers of spiritual penetration are not capable of reach-
ing down into the depths of these motives. And in
practical everyday life our attitude to our fellow beings
is based on the assumption that their words and actions
are determined by distinct causes, which lie in the indi-

104 WHERE IS SCIENCE GOING?

vidual nature itself or in the environment, even though
we admit that the source of these causes cannot be dis-
covered by ourselves.

What do we then mean when we say that the human
will is free? That we are always given the chance of
choosing between two alternatives when it comes to a
question of making a decision. And this statement is not
in contradiction with what I have already said. It would
be in contradiction only if a man could perfectly see
through himself as the eye of God sees through him;
for then, on the basis of the law of causality, he would
foresee every action of his own will and thus his will
would no longer be free. But that case is logically ex-
cluded ; for the most penetrative eye cannot see itself,
no more than a working instrument can work upon
itself. The object and subject of an act of knowing can
never be identical ; for we can speak of the act of know-
ing only when the object to be known is not influenced
by the action of the subject who initiates and performs
the act of knowing. Therefore the question as to
whether the law of causality applies in this case or in
that is in itself senseless if you apply it to the action of
your own will, just as if somebody were to ask whether
he could lift himself above himself or race beyond his
shadow.

In principle every man can apply the law of causality
to the happenings of the world around him, in the spir-
itual as well as in the physical order, according to the
measure of his own intellectual powers; but he can do
this only when he is sure that the act of applying the

NATURE'S IMAGE IN SCIENCE 105

law of causality does not influence the happening itself.
And therefore he cannot apply the law of causality to
his own future thoughts or to the acts of his own will.
These are the only objects which for the individual
himself do not come within the force of the law of
causality in such a way that he can understand its play
upon them. And these objects are his dearest and most
intimate treasures. On the wise management of them
depend the peace and happiness of his life. The law of
causality cannot lay down any line of action for him and
it cannot relieve him from the rule of moral responsi-
bility for his own doings; for the sanction of moral
responsibility comes to him from another law, which has
nothing to do with the law of causality. His own con-
science is the tribunal of that law of moral responsi-
bility and there he will always hear its promptings and
its sanctions when he is willing to listen.

It is a dangerous act of self-delusion if one attempts
to get rid of an unpleasant moral obligation by claiming
that human action is the inevitable result of an inexor-
able law of nature. The human being who looks upon
his own future as already determined by fate, or the
nation that believes in a prophecy which states that its
decline is inexorably decreed by a law of nature, only
acknowledges a lack of will power to struggle and win
through.

And so we arrive at a point where science acknowl-
edges the boundary beyond which it may not pass, while
it points to those farther regions which lie outside the
sphere of its activities. The fact that science thus de-

io6 WHERE IS SCIENCE GOING?

clares its own limits gives us all the more confidence in
its message when it speaks of those results that belong
properly to its own field. But on the other hand it must
not be forgotten that the different spheres of activity of
the human spirit can never be wholly isolated from one
another j because there is a profound and intimate con-
nection between them all.

We started on the territory of a special science and
have dealt with a series of problems that are of a purely
physical character j but these have led us from the
world of mere sense-perception to the real metaphysical
world. And this world faces us with the impossibility of
knowing it directly. It is a land of mystery. It is a world
whose nature cannot be comprehended by our human
powers of mental conception j but we can perceive its
harmony and beauty as we struggle towards an under-
standing of it. And here on the threshold of this meta-
physical world we have been brought face to face with
the highest question of all, that of the freedom of the
human will. It is a question which each one must medi-
tate upon for himself if he thinks at all seriously on
what the meaning of this life may be.

CHAPTER IV
CAUSATION AND FREE WILL

THE PROBLEM STATED

THIS is one of man's oldest riddles. How can the
independence of human volition be harmonized
with the fact that we are integral parts of a universe
which is subject to the rigid order of nature's laws?

At first sight these two aspects of human existence
seem to be logically irreconcilable. On the one hand
we have the fact that natural phenomena invariably
occur according to the rigid sequence of cause and
effect. This is an indispensable postulate of all scien-
tific research, not merely in the case of those sciences
that deal with the physical aspects of nature, but also
in the case of the mental sciences, such as psychology.
Moreover, the assumption of an unfailing causal
sequence in all happenings is the basis on which our
conduct of everyday life is regulated. But, on the other
hand, we have our most direct and intimate source of
knowledge, which is the human consciousness, telling
us that in the last resort our thought and volition are
not subject to this causal order. The inner voice of con-
sciousness assures us that at any given moment we are
capable of willing this or that alternative. And the

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io8 WHERE IS SCIENCE GOING?

corollary of this is that the human being is generally
held responsible for his own actions. It is on this as-
sumption that the ethical dignity of man is based.

How can we reconcile that dignity with the principle
of causation? Each one of us is an integral part of the
world in which we live. If every other event in the
universe be a link in the causal chain, which we call
the order of nature, how can the act of human volition
be looked upon as independent of that order? The
principle of causation is either universally applicable or
it is not. If not, where do we draw the line, and why
should one part of creation be subject to a law that
of its nature seems universal, and another part be ex-
empted from that law?

Among all civilized races the profoundest thinkers
have tackled this problem and have suggested innu-
merable solutions. I have no intention of adding to the
sum-total here. My purpose in taking up the question
in connection with my own science is that the con-
troversy has now entered the scientific field. From
suggestions which have been made as to the inapplica-
bility of the causal principle to certain types of re-
search in physical science extensive conclusions have
been drawn and the age-old controversy is now being
waged more bitterly than ever.

After all the thought that has been expended on it,
since man first began to reason over his place in the
universe, one might justifiably assume that the prob-
lem of causation would be nearer to a solution now than
formerly, even if we grant that a complete and final

CAUSATION AND FREE WILL 109

solution is impossible, from the very nature of the
question itself. And we might reasonably expect that
at this stage of the controversy the disputants would
at least be in agreement as to the nature of the funda-
mental issues under discussion. But the opposite is the
case. Nowadays it is not merely the problem itself that
is debated ; but even the very basic ideas involved in
it are called into question — ideas such as the meaning
of the concept of causality in itself and epistemological
questions regarding the objects which should be con-
sidered to be within the legitimate scope of human
knowledge, the difference between objects that are
sensuously perceptible and objects that are outside this
range and other such questions. All this quarreling over
fundamentals has added to the confusion.

The protagonists are mainly divided into two
schools. One school is interested in the question chiefly
from the viewpoint of the advancement of knowl-
edge, holding that the principle of strict causation is
an indispensable postulate in scientific research, even
including the sphere of mental activity. As a logical
consequence of this attitude, they declare that we can-
not except human activity in any shape or form from
the universal law of causation. The other school is
more concerned with the behavior of human beings
and with the sense of human dignity, which feels that
it would be an unwarrantable degradation if human
beings, including even the mentally and ethically
highest specimens of the race, were to be considered as
inanimate automata in the hands of an iron law of

no WHERE IS SCIENCE GOING?

causation. For this school of thinkers the freedom of
the will is the highest attribute of man. Therefore we
must hold, they say, that the law of causation is ex-
cluded from the higher life of the soul, or at least that
it does not apply to the conscious mental acts of the
higher specimens of humanity.

Between these two schools there is a great number
of thinkers who will not go the whole distance in either
direction. They feel in a certain sense that both parties
are right. They will not deny the logigaj validity of
the one position nor the ^tjrrgl validity of the other.
They recognize that in the mental sciences the prin-
ciple of causation, as a basis of scientific research, is
nowadays being pushed far beyond the borders of in-
animate nature and with advantageous results. There-
fore they will not deny the play of causality in the
mental sphere, though they would like to erect a bar-
rier somewhere within that sphere and entrench the
freedom of human volition behind that barrier.

Among those who do not belong to either of the
extreme schools perhaps I ought also to mention those
scientists who are against the universal application of
the principle of causality in physical science. They
hold that it is inapplicable to the natural phenomena
that are studied in quantum physics. But most of the
scientists who hold this do not question the universal
validity of the principle in itself. Still the attitude
must be mentioned here; because, though it does not
form anything like a school of thought, it indicates a
tendency. And inasmuch as that tendency has been ex-

CAUSATION AND FREE WILL in

ploited by popularizers, who speak of spontaneity in
the inner workings of nature, it deserves to be dealt
with, if for no other purpose than to keep the lines
of communication clear between serious science and the
seriously thinking public.

As to the general controversy itself, if it did not
affect our approach to physical science physicists as
such would not have to concern themselves with the
matter. But the controversy now affects the very basic
method on which scientific research is carried on. If
the basis of causation be not valid, then how can the
decisions arrived at on this basis be considered as re-
liable? Therefore the controversy affects the general
claim to reliability which natural science puts forward.
That is the reason why I am discussing it here as a
physicist, in the hope that what I have to say may help
to keep clear the grounds on which my own branch
of science rests its claim to reliability.

Let us first consider the problem under its general
aspect. What is the significance of the concept under-
lying the expression JLaw of Causation? In everyday
life we are familiar "with tne idea ot a cause and, like
so many everyday things, we imagine that this idea is
the simplest thing in the world to explain. Common
sense and daily experience show us that all things and
events are the products of other things and events.
We say of what happens before our eyes that it is the
effect of something else and we call that something
else the cause, realizing at the same time that several
causes may have contributed to bring about one and

112

WHERE IS SCIENCE GOING?

the same effect. On the other hand, we realize that ef-
fects themselves may be the cause of subsequent events.

When we find ourselves face to face with an event
which we cannot possibly refer to any cause or series
of causes, and which lies outside the range of all the
causes that we are familiar with, then what happens?
Is it perfectly certain and necessary for human thought
that for every event in every instance there must be
a corresponding cause? Would the thought involve a
logical contradiction that in this or thät case the event
has absolutely happened of itself and has no causal
relation whatsoever to any other event? Of course the
answer is in the negative 3 for it is very easy to think
of an event as having no explanatory cause whatsoever.
In such cases we speak of miracles and wonders and
magic. And the simple fact that there exists a whole
range of literature whose scenes are laid in wonderland
is proof in itself that the concept of strict causality is
not an inherent necessity of human thought. Indeed
the human mind finds little difficulty in thinking of
everything in the world as turning topsy-turvy. We
can say to ourselves that to-morrow the sun may rise
in the east, for a change. We can say to ourselves that
a miracle of nature may occur, contrary to all the known
laws of nature. We can think of the Niagara Falls
for instance as shooting upwards, though this would
be impossible in the world of reality. I can think of
the door of my room in which I am now writing as
opening of its own accord. And I can think of historical
personages as entering the room and standing beside

CAUSATION AND FREE WILL 113

my table. In the world of reality to talk of such events
may be meaningless and we may call them impossible,
at least in our everyday way of reasoning. But we must
distinguish this kind of impossibility from a logical
impossibility, such as the idea of a square circle or
that the part of something is greater than the whole,
for no matter what efforts we make to think such
things we cannot think them, inasmuch as they entail
an inner contradiction. We can think of a part and
we can think of the whole to which it belongs but we
cannot think of the part as greater than the whole.
This kind of impossibility is inherent in the nature of
human thought itself, whereas the idea of something
happening outside the range of causation is quite
logically coherent.

Thus from the outset we can be quite clear about
one very important fact, namely, that the validity of
the law of causation for the world of reality is a ques-
tion that cannot be decided on grounds of abstract rea-
soning. But reality, no matter what may be said to the
contrary, is only a particular and small section of that
immense sphere over which human thought can range.
This is true even though our powers of imagination
have always to take their cue from some real experi-
ence. Indeed experience is for us the starting-point of
all thought j but we possess the gift of going beyond
reality in thought. And were it not for this faculty of
the imaginative intellect we should have no poetry and
no music and no art. Indeed it is one of the highest
and most precious gifts that man possesses, this power

114 WHERE IS SCIENCE GOING?

of lifting himself in thought into the realms of light
whenever the weight of everyday life presses upon
him and makes itself intolerable.

The creations of art are similar to those of science
at least to the extent that scientific research, in the
strictest sense of the term, could never advance with-
out the creative force of the imaginative intellect. The
man who cannot occasionally imagine events and con-
ditions of existence that are contrary to the causal prin-
ciple as he knows it will never enrich his science by
the addition of a new idea. And this power of thinking
beyond the range of causation is a prerequisite not only
for the construction of hypotheses but also for the sat-
isfactory coordination of results that have been arrived
at through scientific research. It is the imaginative
vision that puts ; jp£ward an hypothesis. Then comes
experimental research to put~~the hypotnesis to its test.
The results immediately arrived at through experiment
have to be coordinated so as to form the basis of a
theory, in the hope of discovering the laws of nature
underlying the phenomena that have been studied.
This work again calls the imaginative powers into play
and further experiment puts the laws thus constructed
to their final critical test.

To show how the scientific mind must necessarily
imagine alternative happenings that lie outside the
actual range of causation, when it is seeking to estab-
lish its conclusions, let us take a simple example from
natural science as an illustration. Let us think of a ray
of light coming to us from some distant star. Or in-

CAUSATION AND FREE WILL 115

deed we can think of it as coming from some nearer
source, such as an electric lamp. But let us think of it
as passing through many transparent media of differ-
ent nature and different densities, such as air, glass,
water, etc., before it finally reaches the eye. What route
will the light choose in coming from its point of origin
to the eye of the observer? Generally speaking, this
will not be a straight line; because when light passes
through one medium after another its direction is bent
from the direction of the line of entry. We are all
familiar with this phenomenon in the case of a stick
put into water. The line of light coming from the stick
to the eye is bent at the point of emergence. And so
the line of transmission for a beam of light coming
from a distant source to the eye will be bent in each
of the different transparent media through which it
passes 5 so that its course will be zigzag, according to
the number and varying densities of the media. Even
in the atmosphere itself the line which a ray of light
follows is quite irregular, because the atmosphere pos-
sesses different powers of deflection at different
heights.

Now, can we get any formula which states the actual
route which our imaginary ray of light follows? We
can. The answer is very definite. It is contained in that
remarkable law of nature according to which a ray of
light leaving a distant source will always choose, from
the many alternative routes at its disposal, that route
which will bring it to the eye of the observer within
the shortest time, allowing for the fact that the light

n6 WHERE IS SCIENCE GOING?

has to pass through the different media at different
rates of speed. This is called the Principle of Quick-
est Arrival. And it has been a very useful principle in
scientific research. But it would have no meaning what-
soever were we not in a position to imagine other al-
ternative ways through which the light might travel,
though in reality it does not travel along these ways
and therefore they are causally impossible, in the sense
that light cannot actually come by any other route.
All the alternative routes that we may imagine are
possible only in the abstract realm of the brain. They
are impossible in the reality of nature. It is as if the
light possessed a certain amount of intelligence and
acted by the necessity of its own nature on the laud-
able principle of accomplishing its task in the quick-
est possible time. Therefore it has not the opportunity
to dally and try out alternative ways, for it has to
decide at once on the quickest way.

We have other similar cases in natural science such,
for instance, as virtual motions which do not obey
dynamical laws and therefore in the causal sense are
impossible. But all these fanciful constructions play a
very important role in theoretical science. They are
employed as very useful instruments of thought in
the carrying out of researches and the construction of
theories. Therefore they certainly do not involve any
contradiction of the laws of thought itself.

Once we have decided that the law of causality is
by no means a necessary element in the process of
human thought, we have made a mental clearance for

CAUSATION AND FREE WILL 117

the approach to the question of its validity in the world
of reality. Now in the first place let us ask what is
meant by the term, Causation? We might mean by it
a regular interrelation""E>etween effects that follow one
another in time. But we can at once ask whether this
relation be founded in the nature of things themselves,
or is it totally, or partly, a product of the imaginative
faculty? Might it not be that mankind originally de-
veloped this concept of causation to meet the necessi-
ties of a practical life, but afterwards found that if
men were to confine themselves to an outlook exclu-
sively based on this principle life would then turn out
to be unbearable? We need not delay here to discuss
the various philosophical aspects of these questions.
For our present purpose it is much more important to
ask whether the causal connection between events must
be considered as absolutely complete and always un-
broken or are there events in the world which do not
enter the chain as connecting links?

Let us first see whether this question can be settled
by a systematic application ofjdeductive reasoning. As
a matter of fact some of the most famous philosophers
in the history of human thought have produced solu-
tions of the causal problem which were based on purely
abstract grounds. They took their first stand on the
axiom ex nihilo nihil fit, that nothing comes from noth-
ing, in other words that no event in the world holds in
itself an adequate explanation of its own existence.
Reasoning back from this standpoint the philosophers
of what is generally called the rationalist school es-

n8 WHERE IS SCIENCE GOING?

tablished as a logical necessity the existence of a Su-
preme Cause. This Supreme Cause is the God of
Aristotle and the scholastic philosophers. As a logical
consequence of the line of reasoning thus adopted it
was necessary to attribute to this Godhead the pos-
session in their plenitude of all the perfections that are
present in the world. If there be an actually existent
Supreme Cause outside of the world, who is the
Creator of the world and the Creator of all things in
the world, then man can deduce the nature of this Su-
preme Cause only through a study of His handiwork.
From this one can easily see that the nature to be at-
tributed to that Supreme Cause must necessarily depend
upon man's outlook on created things. In other words,
the concept of the Divinity in this case must take its
color from the world outlook either of the individual
philosopher in question or of the particular cultural
background to which he belongs. In the attempt which
the scholastics made to harmonize the Jehovah of the
Jewish culture with the rational God of Aristotle, em-
phasis was laid on the fact that there is no logical con-
tradiction whatsoever in the idea of the Creator
interposing his hand suddenly within the order of His
own creation, and thus we have belief in miracles and
wonders established on a philosophical basis. There-
fore in the philosophy of the historic rationalist school,
though the order of nature is admitted as inevitably
predetermined by the Supreme Cause, yet the causal
chain in the world itself may at any time be inter-
rupted by the intervention of a supernatural power.

CAUSATION AND FREE WILL 119

We pass now from the Greco-scholastic to the mod-
ern philosophical concept of the world. Rene Descartes
is generally considered to be the father of modern
philosophy. According to Descartes, God made all the
laws of nature and all the laws that govern the human
spirit by an act of His own free will and for purposes
which are so recondite that human thought is unable
to penetrate to their full meaning. Therefore in Car-
tesian philosophy the possibility of miracles is by no
means excluded. Moreover, the logical consequence of
the inscrutability of God's design in the world is that
we must admit the possibility of events the understand-
ing of which lies entirely outside of the range of the
human intellect. These may be called mysteries rather
than miracles in the scholastic sense of the latter term.
In other words, as our minds are not capable of en-
compassing the laws which guide the universe we must
be content to treat certain happenings as beyond all our
power of explanation and referable only to the mys-
terious ways of Divine Providence. For the purpose of
science this means that practically we must admit the
existence of breaks in the causal chain.

In contradistinction to the Cartesian Divinity, the
God of Baruch Spinoza is a God of harmony and
order, whose nature so interpenetrates all creation that
the universal causal relation is itself divine and there-
fore absolutely perfect and permitting of no excep-
tions. In Spinoza's view of the world there is no room
for accident or miracle. That is to say, the causal in-
terrelation is absolutely unbroken.

120 WHERE IS SCIENCE GOING?

The next great name that comes into view, when
looking over the various world philosophies which
were founded on a rationalistic basis, is that of Gott-
fried Wilhelm Leibniz. According to Leibniz the world
was made in fulfillment of a plan corresponding to the
supreme wisdom of the Creator. In every created thing
God implanted the law of its own individual being, so
that each being in the world is independent of and
develops independently of all other things, following
only the law of its own individual destiny. Therefore,
according to Leibniz, the causal interrelation between
one thing and another is only apparent. This means
that we must exclude the principle of causation.

We may conclude, I think, from these few examples
that the philosophical theories rationally deduced from
abstract principles, as regards the place of the causal
principle in the world, are almost as numerous as the
philosophers themselves. It is obvious that along this
road we can make no progress towards a solution of
the general problem.

Now we come to a break in the philosophical tra-
dition. Whatever may be said against the English em-
piricist school and its solipsist 1 consequences at least
it made a break with the naive conceits of the traditional
rationalist school and opened up the way to the devel-
opment of a philosophical outlook which is more in
harmony with the scientific view of the world. The
outstanding characteristic in the teaching of the Eng-
lish empirical school is that there is no such thing as

1 Solipsism is the theory that the only conscious being is myself.

CAUSATION AND FREE WILL 121

certain knowledge or innate ideas, such as were pre-
sumed by some of the earlier rationalist philosophers.
The human mind as it comes into the world is an abso-
lute blank, on which sense-given impressions are au-
tomatically recorded without any action on the part
of the mind itself.

John Locke was the founder of this school. He rep-
resents the first systematic attempt to estimate in a
critical way the certainty and adequacy of human
knowledge when confronted with the universe around
it. According to Locke all ideas ultimately depend on
experience and by experience Locke means the sensory
perceptions of the five senses. Beyond these five senses
there is only the reflective consciousness, which is not
a sense, as having nothing to do with objects, but as
Locke says "it may properly enough be called an in-
ternal sense." What we feel to be warm or cold or hard
or soft and what we see to be red or blue, that we
know; and no other special definition of it is necessary
or indeed possible. One often hears of a delusion of
the senses, as may happen in the case of a mirage, for
instance. This, however, does not imply thaFthe sensa-
tion itself is mistaken, but rather that the conclusions
which we draw from the sensory perception are incor-
rect. What deceives us is not the perceptive sense but
the rationalizing intellect.

Sensory perception is something entirely subjective
and therefore from this we cannot deduce the existence
of the object. Green is not a property of the leaf but
a sensation which we experience on looking at the leaf.

122 WHERE IS SCIENCE GOING?

And so it is with the other senses. Remove the sense-
impressions and nothing of the object will remain. John
Locke seems to have thought that the sense of touch
plays a more important role than the other senses, be-
cause it is through this sense that we perceive the me-
chanical qualities of bodies such as thickness, extension,
form and movement, and Locke seems to attribute
these qualities to something in the bodies themselves.
But the later empiricists, especially David Hume, held
that all mechanical qualities of bodies existed only in
the senses of the perceiving subject.

In the light of this theory the so-called outer world
resolves itself into a complex of sense-impressions and
the principle of causation signifies nothing more than
a certain order experienced in the sequence of one
sensation after another. The idea of order is itself a
sense-impression which must be taken as something im-
mediately given and which does not permit of further
analysis, for that order may come to an end at any mo-
ment. Therefore there is no causation. One thing is
observed to follow another but observation cannot
assert that it is "caused" by that other thing.

If a rapidly moving billiard-ball strikes against an-
other and sets the latter in motion we experience two
independent sense-impressions, one after the other:
namely the sensory perception of the moving billiard-
ball and the sensory perception of the one set in mo-
tion by it. If we stand beside the billiard-table as the
play goes on these observations are repeated and we
can register a certain regularity between the impres-

CAUSATION AND FREE WILL 123

sions. For instance, we can perceive that the velocity
of the second billiard-ball depends upon the velocity
and mass of the billiard-ball that strikes it. We can
discover also a further order between these two phe-
nomena. We can, for instance, measure the noise of
the impact by its force and we can detect the momen-
tary flattening on each ball at the point of contact with
the other ball if we smear one of the balls with some
colored material. All these, however, are only so many
sense-perceptions which accompany one another regu-
larly or displace one another regularly. But they are
such that there is no logical connecting-link between
the one and the other. If we speak of the force which
the moving billiard-ball exercises on the one that is at
rest, this is only an analogy concept which arises
through the muscular sensation which we feel if we
ourselves move the ball that is at rest with the naked
hand rather than through the medium of the moving
billiard-ball. The concept of force has been very use-
ful for the formulation of the laws of motion, but
from the viewpoint of knowledge it helps nothing
whatsoever. And this is because we have no way of
joining up, through a causal bond or a logical bridge,
the different phenomena of motion that we have ex-
perienced. The individual sense-impressions are differ-
ent and will remain different, no matter what relations
between them may be perceived.

Here the meaning of the principle of causation,
taken fundamentally, lies simply in the statement that
from the same or similar sensory complexes as cause

124 WHERE IS SCIENCE GOING?

the same or similar sensory complexes will follow as
an effect; but herein the question as to what may be
looked upon as similar will on each occasion demand
special proof. Formulated in this way, the principle
of causation is deprived of all deeper meaning. But
this of course does not mean that the law of causation
has no practical significance for the human reason. All
it means is that the postulate of causation does not fur-
nish us with the grounds of any certain knowledge.

How then can the fact be explained that in common
everyday life we take the causal relation of things as
something objective and independent? How can this
be if in reality we experience nothing more than orderly
successions of individual sense-perceptions? The teach-
ing of empirical skepticism answers that this happens
through the enormous utility of the causal concept and
through the force of habit. Habit certainly plays an
important part in life. From childhood onwards it in-
fluences our temperament, our wills and our thought.
We think we understand a thing merely because we
have become accustomed to looking at it. The first time
* that something new strikes us we feel surprised y but
if the same thing happened for the tenth time we find
it quite a natural happening. If it should happen a
hundred times we say that it is obvious and we even
go the length of looking upon it as a matter of neces-
sity. Over one hundred years ago or so mankind in
general was acquainted with no other locomotive force
except the muscular force of man and beast. As a con-
sequence, no other form of force was considered pos-

CAUSATION AND FREE WILL 125

sible. The pressure of the air and falling water was
recognized and applied to mechanical purposes. But
here the force itself was stationary and not locomotive
in the arbitrary sense. Only men and animals by their
muscular effort could move at will from one place to
another. A story is told that when the first railways
were seen running through the countryside the peas-
ants betted with one another as to how many horses
were concealed in the engine. With steam and electric
motors everywhere our youth of to-day cannot easily
understand the mentality of the peasant of one hun-
dred years ago who felt the necessity of attributing
locomotive transport exclusively to a natural horse
power.

So far the skeptics are right in saying that it is by
force of habit and custom that we attribute certain
happenings to certain causes. But at the same time this
force of habit cannot explain why we should make the
attribution at all. In Fritz Reuter's story Rei's Nah
Belligen, the peasants undoubtedly made a ludicrous
mistake in supposing that there were horses concealed
in the steam engine, just as the ancient Greek peasant
made a mistake in attributing the thunder to the per-
sonal anger of Jupiter. But this is not the point here.
The point rather is to answer the question why these
events should be attributed to a cause at all and how
it is that the concept of causation itself arises when we
see one event following another. The mere regular
succession of impressions does not explain this.

If we go a little deeper into the consideration of the

126 WHERE IS SCIENCE GOING?

empiricist theory and ask where it would finally lead
us were we to pursue it to its logical consequences we
shall thus be putting it to a practical test. In the first
place we must bear in mind the fact that when there
is question of sensory perception as the sole and ex-
clusive source of knowledge, then there can be ques-
tion only of each one's personal sensory perception
in each one's own consciousness. That other men have
similar perceptions we can assume only by analogy; but,
on the empiricist theory, we cannot know this nor can
we logically prove it. Therefore if we are to abide by
the logical consequences of the empirical doctrine and
exclude all arbitrary assumption, we must confine our-
selves, each one of us, to the grounds of his or her
own personal sense-perceptions. Then the principle of
causation is only a framework for our experiences, con-
necting them with one another as they enter through
the senses and, being entirely unable to tell us anything
of what is to come next, it cannot tell us whether the
sequence of our experiences may not be broken in a
moment. This condition of affairs would seem to ob-
literate every line of distinction between the sensory
perceptions arising from the world of ordinary hap-
penings and those that have no foundation whatsoever
in that world. Take the case of sleep for instance. I
may dream all sorts of things during the night j but
the moment I wake up the reality of my surroundings
gives the lie to the dream. The empiricist, however,
cannot logically admit that. For him there is no wak-
ing reality j because the subjective sensation is the sole

CAUSATION AND FREE WILL 127

source of awareness in consciousness and is the sole
basis and criterion of knowledge. Now the dreamer
during the dream believes automatically in its reality
and, according to the empiricists, the wide awake person
believes automatically in the reality of his sense-
perceptions, but has no more reason than the dreamer
has for saying that one set of perceptions is false and
the other true.

On the grounds of pure logic of course this system
of thought, which is commonly called solipsism, is im-
pregnable. The solipsist establishes his ego at the cen-
ter of creation, and he does not consider any knowledge
as real or sound except that which he for the moment
is receiving through his sensory perception. Everything
else is derivative and secondary. When the solipsist goes
to sleep at night the world ceases to exist for him the
moment his eyes and ears and sense of smell and touch
become inactive. On rising in the morning everything
is new to him again. Here of course I am only imagin-
ing what a human being would be if he were a logical
consequence of the empirical teaching.

All this of course amounts to a repudiation of com-
mon sense j so much so that even the most advanced
skeptics of this school find themselves constantly com-
promising between the claims of common sense and
the purely logical conclusions of their own philosophic
system. In this connection it is interesting to call at-
tention for a moment to the figure of one of the most
outstanding personalities in the subjectivist school,
namely, Bishop Berkeley. As a student Berkeley studied

128 WHERE IS SCIENCE GOING?

Locke. But he was of a very deep religious nature and
launched a strong criticism against Locke's philosophy
because of its skepticism. For Berkeley all things exist
only in the mind and the external world can be ac-
counted for only by saying that it exists in the mind
of God. He arrives at the existence of God in this way:
There are in our own consciousness impressions which
are independent of our own wills and sometimes exist
even contrary to our wishes. For these impressions we
must seek a cause elsewhere than in ourselves, and so
Berkeley is led to establish the existence of God by
practically the same line of reasoning as the rationalist
school. For him, however, mind and mind alone exists
— the Divine Mind and the human mind. The world
of reality as we perceive it exists only in our own mind.
Therefore with Berkeley we have no right to talk about
a causal interrelation between things in the outer world
of reality.

To sum up, empiricism is unassailable on the funda-
mental ground of a pure logic ; and its conclusions are
equally impregnable. But if we look at it purely from
the viewpoint of knowledge it leads into a blind alley,
which is called solipsism. In order to escape from this
impasse there is no other way open but to jump the
wall at some part of it, and preferably at the begin-
ning. This can be done only by introducing, once and
for all, a metaphysical hypothesis which has nothing
to do with the immediate experience of sense-percep-
tions or the conclusions logically drawn from them.

Immanuel Kant, the founder of the critical school,

CAUSATION AND FREE WILL 129

was the first to recognize this truth clearly and to point
out the way in which the metaphysical step must be
taken. According to Kant, the sense-impressions in our
consciousness are not the only source of knowledge.
The mind has certain concepts that are independent of
all experience. These are the so-called categories 5 and
in the philosophy of Kant they are a necessary condi-
tion of all knowledge. Kant concluded that causality
is such a category. It is one of the ultimate a priori
forms in which the understanding spontaneously orders
its experience — something that is not a derivative from
experience but on the contrary is necessary to make
orderly experience itself possible. Kant formulated the
principle of causality in this way: "Everything that
happens presupposes something from which it follows
according to a law." Kant held that this postulate is
independent of all experience. But Kant's proposition
cannot be stated by saying that everything which regu-
larly follows something else has a causal relation to
that thing. For instance, there scarcely can be a more
regular succession than that of night following day 5
but nobody would assert that the day is the cause of
the night. Succession therefore is not of itself, as with
the empiricists, the same as a causal relation. In the
example given, namely that of day and night, we have
two effects which follow from the same cause. This
cause is twofold. It consists on the one hand of the /
earth's rotation on its axis and, on the other hand, of /
the fact that the earth is opaque to the sun's rays.
In the Kantian system therefore the universal '

130 WHERE IS SCIENCE GOING?

validity of the principle of causation is asserted. At the
same time, however, it cannot be denied that Kant's
teaching, though useful and conclusive in most of its
results, is to a certain extent arbitrary on account of
its strong dogmatic attitude. This is the reason why
it became the subject of so much direct attack and has
been altered somewhat with the course of time.

We need not trouble ourselves here with a detailed
description of the development of the philosophical
side of the causal problem since the time of Kant. It
will be sufficient to point out the main features of this
development. The strongest opposition to the Kantian
doctrine came from the side of those philosophers who
maintained that it went too far into the metaphysical
field. Now it is perfectly true of course that we cannot
avoid metaphysics if we are to save ourselves from
falling into the deadlock of solipsism ; but, on the other
hand, in so far as any system attempts to avoid the
metaphysical extreme on the one side and the solipsist
extreme on the other, it must be somewhat in the na-
ture of a compromise with logic and therefore will
present certain weak features. It is quite possible, how-
ever, to construct a system on this basis of compromise
wherein the weaker features can be sufficiently strength-
ened for all practical purposes.

Kant's teaching, and with it the whole of transcen-
dental philosophy from idealism to extreme material-
ism, is from the outset based on admittedly metaphysical
grounds. In contradistinction to this, the positivist sys-
tem, founded by Auguste Comte, has maintained itself

CAUSATION AND FREE WILL 131

as free as possible in its various shapes and forms from
metaphysical influences. It achieves this end by making
the experience of our own consciousness the only
legitimate source of knowledge. According to the posi-
tivist teaching, causality is not founded in the nature
of things themselves but is, to put it briefly, an experi-
ence of the human mind. It plays an important role
principally because it has proved itself fruitful and
useful. Thus the law of causality is the application of
this experience. Because we can always exactly know
what we ourselves have discovered by our own experi-
ence, the meaning of the causal concept is quite clear
to us. But at the same time the possibility remains that
there may be cases to which our discovery is not ap-
plicable and which therefore contradict the law of
causation. Whereas Kant teaches that knowledge with-
out causality is impossible from the very outset, be-
cause the category of the causal concept was already
in the human mind previous to any experience, the
positivist standpoint is that the creative mind of man
has fashioned the causal concept for its own conven-
ience. Therefore it is not a primal, inborn quality in
the mind. "Man is the measure of all things," said
Protagoras long ago. We can twist and turn as we will
but we can never get out of our own skins. And what-
ever tangent we may fly off at into the realm of the
absolute we are always really moving around within our
own orbit, which has been prescribed for us by the
range of experience perceived in our own conscious-
ness. To a certain extent it is not possible to gainsay

132 WHERE IS SCIENCE GOING?

this positivist attitude, though from the standpoint of
transcendental philosophy there are many objections
to it. And so argument and counter-argument follow
one another in an endless interchange. For us the
denouement of the story is the confirmation of our
previous conviction, namely, that the nature and uni-
versal validity of the Law of Causation cannot be
definitely decided upon any grounds of purely abstract
reasoning. The transcendental and positivist viewpoints
are irreconcilable and they will remain so as long as
the race of philosophers lasts.

If pure reasoning had the last word in dealing with
such cases then the outlook would be hopeless for any
satisfactory settlement of the causative problem. But
philosophy, after all, is only one branch of human ac-
tivity in the study of problems affecting nature and
mankind. Science is another branch. And where philoso-
phy has failed in a given instance we are perfectly
justified in turning to science and asking whether it
may not have a satisfactory answer to suggest.

Now, let us first ask whether the various branches
of science are divided against one another on this ques-
tion of causation, just as philosophy is divided? At
the very threshold of this inquiry it may be objected
that a problem which falls within the scope of philoso-
phy and which philosophy fails to solve cannot pos-
sibly be solved within the limits of a single science.
This objection is urged on the grounds that philosophy
furnishes the mental foundations on which scientific
investigation rests. Philosophy must precede every spe-

CAUSATION AND FREE WILL 133

cial science and we should be going against the grain
of our whole mental discipline if one of the special
sciences were to take up the treatment of general philo-
sophic questions.

That argument is very often urged. But in my opin-
ion the weakness of it is that it leaves out of considera-
tion the collaboration which actually exists between
philosophy and the various special sciences. We must
remember that the starting-point of all investigation
and the mental equipment used in the pursuit of it are
fundamentally the same in the case of philosophy as
in the case of science. The philosopher does not oper-
ate with a kind of human understanding that is special
to himself. The structure of thought which he builds
up is not based on any other foundation except that
of his daily experience and the opinions which he has
formed during the course of his professional studies.
These latter must largely correspond to his individual
talents and the background of his personal philo-
sophical development. In a certain sense the philoso-
pher is in a much higher position than the scientific
specialist, because the latter confines observation and
research to a much narrower range of facts that are
systematically assembled and call for a deep and con-
centrated kind of probing. Therefore the philosopher
has a better outlook on general relations which do not
immediately interest the scientific specialist and which
may easily pass unobserved by the latter.

The difference between the outlook and work of
these two types of investigation may be compared to

134 WHERE IS SCIENCE GOING?

the case of two travelers who visit the same district
together. The first traveler, let us say, is interested
in the general features of the landscape, the undula-
tions of hill and valley, and the varying patterns of
forest and meadowland. The second traveler is inter-
ested only in the flora and fauna or possibly only in
the mineral products of the region. His eyes are watch-
ing for particular specimens of the former, or he may
select various patches of ground for scientific examina-
tion in the hope of discovering the presence of mineral
wealth beneath. Now the first traveler certainly ac-
quires a better knowledge of the landscape as a whole
and can contrast it with other landscapes. From a gen-
eral view he may conclude in a general way as to the
mineral qualities of the soil and the kind of vegetation
or animal life that characterize it; but his deductions
would be quite general and will depend for verification
and clarity of statement on the opinion supplied to him
by his companion. Therefore the work of the one is
complementary to the work of the other ; and there may
be innumerable instances wherein the work of the sec-
ond traveler will be absolutely necessary to the solution
of problems which have baffled the man with the more
general outlook.

This comparison, like every other comparison, is not
fully adequate to the situation. But at least it brings
out this point, namely, that in the case of a definite
problem which philosophy recognizes as fundamental
and the final solution of which is the business of
philosophy alone, where philosophy cannot come to a

CAUSATION AND FREE WILL 135

decisive formulation by the use of its own methods it
must seek information from the special branches of
science in regard to particular features of the problem
at issue. Now if the answer here turned out to be defi-
nite and final then it must be treated as such. It is a
characteristic mark of every true science that the gen-
eral and objective knowledge which it arrives at has
a universal validity. Therefore the definite results
which it obtains demand an unqualified acknowledg-
ment and must always hold good. The progressive dis-
coveries of science are definite and cannot permanently
be ignored.

This is shown very clearly in the development of
natural science. By means of wireless telegraphy we
can now send whatever news we wish to the most
distant parts of the earth within the infinitesimal frac-
tion of a second. Modern man can lift himself into
the air in an aeroplane and transport himself from
one part of the globe to the other, over valley and
mountain and lake and ocean. By means of X-rays he
can pry into the secret activities and inner functions of
living organisms and can discover the location of indi-
vidual atoms in the crystal. This objective achievement
which science has accomplished, in collaboration with
the technique that it has fertilized, has thrown into the
shade some of the greatest discoveries of the philoso-
phers of past times and made a laughing-stock of the
crude arts of the magician.

Were anybody to close his eyes to such tangible re-
sults and talk about the collapse of science, people in

136 WHERE IS SCIENCE GOING?

general would not think of taking the trouble to refute
him. There is no need whatsoever to bring forward any
elaborate proof of the contribution to the advance-
ment of knowledge which science has to its credit. It is
sufficient merely to point to the events that are before
everybody's eyes. One has only to look up when
sitting in one's garden and call attention to the drone
of the aeroplane or to turn on a switch in one's study
and bid the skeptic listen to voices that are coming from
a distance of thousands of miles. The worth of any
human endeavor is and always must be the results which
it has obtained.

Now let us return to the particular problem that we
are dealing with and let us admit for the moment the
competence and reliability of the scientific method in
the treatment of it. Let us ask how does science, in
each of its different branches, actually regard the prob-
lem of causation. Here it must be remembered that I
am talking of specialized science as such and not of
the philosophical or epistemological foundations on
which it works. Does science as a matter of fact occupy
itself exclusively with data immediately given by
sensory impressions and their systematic organization
according to laws of reason? Or does it at the very
outset of its activities reach out beyond the knowledge
given us by this immediate source and make, as it were,
a jump into the metaphysical sphere?

I do not think that there can be any doubt whatso-
ever as to the answer. The first alternative is ruled out
and the second affirmed in the case of each special sei-

CAUSATION AND FREE WILL 137

ence. Indeed it may be said that every individual
science sets about its task by the explicit renunciation
of the egocentric and anthropocentric standpoint. In
the earlier stages of human thought mankind turned
its attention exclusively to the impressions received
through the senses, and primitive man made himself
and his own interests the center of his system of rea-
soning. Confronted with the powers of nature around
him, he thought that they were animated beings like
himself and he divided them into two classes, the one
friendly and the other inimical. He divided the plant
world into the categories of poisonous and non-poison-
ous. He divided the animal world into the categories
of dangerous and harmless. As long as he remained
bound within the limits of this method of treating his
environment it was impossible for him to make any
approach towards real scientific knowledge. His first
advance in this knowledge was accomplished only after
he had taken leave of his own immediate interests and
banished them from his thought. At a later stage he
succeeded in abandoning the idea that the planet
whereon he lives is the central point of the universe.
Then he took up the more modest position of keeping
as far as possible in the background, so as not to in-
trude his own idiosyncrasies and personal ideas between
himself and his observations of natural phenomena. It
was only at this stage that the outer world of nature
began to unveil its mystery to him, and at the same
time to furnish him with means which he was able
to press into his own service and which he could never

138 WHERE IS SCIENCE GOING?

have discovered if he had continued looking for them
with the candlelight of his own egocentric interests.
The progress of science is an excellent illustration of
the truth of the paradox that man must lose his soul
before he can find it. The forces of nature, such as
electricity for instance, were not discovered by men
who started out with the set purpose of adapting them
for utilitarian purposes. Scientific discovery and sci-
entific knowledge have been achieved only by those
who have gone in pursuit of it without any practical
purpose whatsoever in view. The few examples that
I have mentioned make this abundantly clear. Hein-
rich Hertz, for instance, never dreamt that his dis-
coveries would have been developed by Marconi and
finally evolved into a system of wireless telegraphy.
And Roentgen could never have called up a vision of
the immense range of beneficial purposes to which the
X-rays are applied to-day.

I have said that the first step which every specialized
branch of science takes consists of a jump into the region
of metaphysics. In taking this jump the scientist has
confidence in the supporting quality of the ground
whereon he lands, though no system of abstract reason-
ing could have previously assured him of that. In other
words, the fundamental principles and indispensable
postulates of every genuinely productive science are not
based on pure logic but rather on the metaphysical hy-
pothesis— which no rules of logic can refute — that there
exists an outer world which is entirely independent of
ourselves. It is only through the immediate dictate of

CAUSATION AND FREE WILL 139

our consciousness that we know that this world exists.
And that consciousness may to a certain degree be called
a special sense. And one may go even so far as to say
that the existence of the exterior world strikes the con-
sciousness of each individual in some particular way. It
is as if we looked at some distant object through a pair
of glasses and as if each one were wearing glasses of a
slightly different shade of color. And we must take
this into account when we deal scientifically with natural
phenomena. The first and most important quality of all
scientific ways of thinking must be the clear distinction
between the outer object of observation and the sub-
jective nature of the observer.

Once the scientist has begun by taking his leap into
the transcendental he never discusses the leap itself nor
worries about it. If he did science could not advance so
rapidly. And anyhow — which is fundamentally a con-
sideration of no less importance — this line of conduct
cannot be refuted as inconsistent on any logical grounds.

Of course there is the positivist theory that man is the
measure of all things. And that theory is irrefutable in
so far as nobody can object on logical grounds to the
action of a person who measures all things with a human
rule, and resolves the whole of creation ultimately into
a complex of sensory perceptions. But there is another
measure also, which is more important for certain prob-
lems and which is independent of the particular method
and nature of the measuring intellect. This measure is
identical with the thing itself. Of course it is not an im-
mediate datum of perception. But science sets out con-

140 WHERE IS SCIENCE GOING?

fidently on the endeavor finally to know the thing in
itself, and even though we realize that this ideal goal
can never be completely reached, still we struggle on
towards it untiringly. And we know that at every step
of the way each effort will be richly rewarded. The his-
tory of science is at hand to confirm our faith in this
truth.

Having once assumed the existence of an independent
external world, science concomitantly assumes the prin-
ciple of causality as a concept entirely independent of
sense-perception. In applying this principle to the study
of natural phenomena science first investigates if and
how far the law of causal relation is applicable to the
various happenings in the world of nature and in the
realm of the human spirit. Science finds itself here ex-
actly on the same footing which Kant took as the start-
ing-point of his theory of knowledge. As in the case of
Kantian philosophy, so also in the case of each special
branch of science the causal concept is accepted at the
outset as belonging to those categories without which no
progress in knowledge can be made. But we must make
a certain differentiation here. Kant took not merely the
concept of causality but also to a certain degree the
meaning of the causal law itself as an immediate datum
of knowledge and therefore universally valid. Special-
ized science cannot go thus far. It must rather confine
itself to the question as to what significance the law of
causality can be proved to have in each individual case,
and thus through research give practical meaning and
value to the empty framework of the causal concept.

CHAPTER V
CAUSATION AND FREE WILL

THE ANSWER OF SCIENCE

WE now come to ask whether and how far science can
help us out of the obscure wood wherein philoso-
phy has lost its way. What is the practical attitude adopted
by the special sciences in regard to the universal and in-
variable validity of the law of causation? Does science
in its everyday investigations accept the principle of
causation as an indispensable postulate? Does it act upon
the assumption that there are no loopholes in the caus-
ally governed order of nature? Or, while using the
principle as a working hypothesis, does scientific practice
intimate that there are certain happenings in nature
where the law of causation does not function, and that
there are regions in the mental sphere where the causal
writ does not run? In our endeavor to find a definite
answer to those questions we shall have to put them
singly to each of the several branches of specialized
science. In doing this of course we shall have to be con-
tent with quite a summary cross-examination. What has
physical science to say to our problem? What has the
science of biology to answer? And what have the hu-
manist sciences, such as psychology and history, to say?

141

142 WHERE IS SCIENCE GOING?

Let us begin with the most exact of the natural sci-
ences, namely, physics. In classical dynamics, among
which we must include not only mechanics and the
theory of gravitation, but also the Maxwell-Lorentz
view of electrodynamics, the law of causality has been
given a formulation which for exactitude and strictness
may be considered almost as ideal, even though it may
be somewhat one-sided. It is expressed in a system of
mathematical equations through which all happenings
in any given physical picture can be absolutely predicted
if the time and space conditions are known — that is to
say, if the initial state be known and the influences which
are brought to bear upon the picture from outside. To
put the matter in a more concrete way: according to the
law of causation as expressed in the equations of classi-
cal dynamics, we can tell where a moving particle or
system of particles may be located at any given future
moment if we know their location and velocity now and
the conditions under which the motion takes place. In
this way it was made possible for classical dynamics to
reckon beforehand all natural processes in their indi-
vidual behavior and thus to predict the effect from the
cause. The last significant advance which classical dy-
namics achieved in our day came about through the gen-
eral relativity theory of Einstein. This theory welded
together Newtonian gravitation and Galileo's law of in-
ertia. Several attempts have been made recently to show
that the relativity theory corroborates the positivist atti-
tude and in a cerain sense is incompatible with transcen-
dental philosophy. These attempts are entirely mistaken.

THE ANSWER OF SCIENCE 143

For the foundation of the relativity theory is not based
on the rule that all time and space dimensions have only
a relative meaning, which is determined by the reference
system of the observer. The foundation of the relativity
theory lies in the fact that in the four-dimensional space-
time manifold there is a measure, namely the distance
between two points approximating with infinite close-
ness. This is the so-called Tensor or Massbestimmung,
which for all measuring observers and for all reference
systems has the selfsame value, and it therefore is of
a transcendental character entirely independent of any
arbitrary action of the human will.

Into this harmonized system of classical-relativist
physics, however, the quantum hypothesis has recently
introduced a certain disturbance, and one cannot yet defi-
nitely say what influence the subsequent development
of the hypothesis may have on the formulation of fun-
damental physical laws. Some essential modification
seems to be inevitable ; but I firmly believe, in company
with most physicists, that the quantum hypothesis will
eventually find its exact expression in certain equations
which will be a more exact formulation of the law of
causality.

Besides dynamical laws applied to individual cases,
physical science recognizes other laws also, which are
called statistical. These latter express to a fairly accurate
degree the probability of certain happenings occurring
and therefore they allow for exceptions in particular
cases. A classical example of this is the conduction of
heat. If two bodies of different temperatures be brought

144 WHERE IS SCIENCE GOING?

into contact with one another then, according to the two
laws of thermodynamics, the heat energy will always
pass from the warmer to the cooler body. We know
to-day from experiment that this law is only a proba-
bility 3 because, especially when the difference of tem-
peratures between two bodies is exceptionally small, it
may well happen that at one or other particular point of
contact and at one particular moment of time the con-
duction of heat will take place in the opposite direction
— that is to say, from the cooler to the warmer body.
The second law of thermodynamical, as in the case of
all statistical laws, has an exact significance only for
average values arising from a great number of similar
happenings and not for each happening itself. If we are
to consider the individual happening we can speak only
of a definite measure of probability. The case here is
quite similar to the case of a non-symmetrical cube used
in playing with dice. Let us suppose that the center of
gravity of the cube is not at the center of the body but
lies definitely towards one of the sides ; then it is likely
though by no means certain that when the cube is thrown
it will come to rest on that side. The smaller the dis-
tance of the center of gravity from the symmetrical cen-
ter of the cube the more variable will the result be.
Now if we cast the dice sufficiently often and observe
what happens in each case, then we can arrive at a law
which will tell us that the dice will fall on a certain
side so many times out of a thousand, for instance.

Let us return to the example of heat conduction and
ask whether the strict validity of the causal law holds

THE ANSWER OF SCIENCE 145

for individual cases. The answer is that it does hold;
because more thoroughgoing methods of investigation
have proved that what we call transfer of heat from
one body to another is a very intricate process, unfolding
itself through innumerable series of particular processes
which are independent of one another and which we call
molecular movements. And investigation has further
shown that if we presuppose the validity of dynamical
laws for each of these particular happenings — that is to
say, the law of strict causality — then we can arrive at the
causal results through this type of observation. In poinF^
of fact, statistical laws are dependent upon the assump- I
tion of the strict law of causality functioning in each I
particular case. And the non-fulfillment of the statisti-
cal rule in particular cases is not therefore due to the
fact that the law of causality is not fulfilled, but rather
to the fact that our observations are not sufficiently deli-
cate and accurate to put the law of causality to a direct
test in each case. If it were possible for us to follow the
movement of each individual molecule in this very intri-
cate labyrinth of processes, then we should find in each
case an exact fulfillment of the dynamical laws.

In speaking of physical science under this aspect we
must always distinguish between two different methods
of research. One is the macroscopic method, which deals
with the object of research in a general and summary
manner. The other is the microscopic method, which is
more delicate and detailed in its procedure. It is only
for the macroscopic observer — that is to say, the man
who deals with big quantities in a wholesale way — that

146 WHERE IS SCIENCE GOING?

chance and probability exist in regard to single elements
in the object that he handles. The extent and importance
of the chance elements is of course dependent on the
measure of knowledge and skill which is brought to
bear on the object. On the other hand, for the micro-
scopic investigator only accuracy and strict causality exist.
His livelihood depends, as it were, on the quality of
each individual item that he deals with in detail. The
macroscopic investigator reckons only with mass values
and knows only statistical laws. The microscopic investi-
gator reckons with individual values and applies to them
dynamical law in its full significance.

Suppose we consider again the example of the dice
which I have mentioned already. And suppose we treat
it microscopically. This means that together with the
nature of the dice itself — its non-symmetrical character
and the exact location of its center of gravity — we also
take into account its initial position and its initial velocity
and the influence of the table on its movement, the re-
sistance of the air and every other peculiarity that may
affect it — supposing we could examine all these mi-
nutely then there could be no question of chance j be-
cause eacTf time we can reckon the place where the dice
would stop and know in what position it would rest.

Without going into any further details, let me say
that physical science applies the macroscopic method of
research to all happenings where molecules and atoms
are concerned. But it naturally strives to refine its treat-
ment towards the microscopic degree of delicacy and
always seeks to reduce statistical laws to a dynamic and

THE ANSWER OF SCIENCE 147

strictly causal system. Therefore it may be said here
I that physical science, together with astronomy and chem-
istry and mineralogy, are all based on the strict and uni-
versal validity of the principle of causality. In a word,
this is the answer which physical science has to give to
the question asked at the beginning of the present
chapter.

Let us come now to the science of biology. Here the
conditions are very much more intricate, because biology
deals with living things and the problem of life has
always presented very serious difficulties for scientific
research. Of course I cannot speak with special authority
in this branch of science. Yet I have no hesitation in say-
ing that even in the most obscure problems, such as the
problem of heredity, biology is approaching more and
more to the explicit assumption of the universal validity
of causal relations. Just as no physicist will in the las?'
resort acknowledge the play of chance in inanimate na-
ture, so no physiologist will admit the play of chance in
the absolute sense, although of course the microscopic
method of research is very much more difficult to carry
out in physiology than in physics. For this latter reason
the majority of physiological laws are of a statistical
character and are called rules. When an exception occurs
in the application of these empirically established rules,
this is not attributed to any skip or failure in the causal
relation but rather to a want of knowledge and skill in
the way that the rule is applied. The science of biology
sets its face against permitting exceptions as such to
exist. What appear to be exceptions are carefully re-

148 WHERE IS SCIENCE GOING?

corded and collated and are further studied until they
are cleared up in the light of causal relations. Very often
it happens that this further study of exceptions shows
interrelations which were hitherto unthought of, and
throws a new light on the rules under which the excep-
tions were originally found to occur. It very often hap-
pens that the universal causal relation is thus corrobo-
rated from a new side, and that is the way in which
many significant discoveries have been made.

How can we distinguish between what is veritably a
causal relation and what is merely a coincidence or ex-
ternal succession of one event following another? The
answer is that there is no hard and fast rule for making
such a distinction. Science can only accept the universal
validity of the law of causation, which enables us defi-
nitely to predict effects following a given cause, and in
case the predicted effect should not follow then we know
that some other facts have come into play which were
left out of consideration in our reckoning. A little story
will illustrate my meaning here. It refers to the effi-
ciency of artificial manure in agriculture.

If I am not mistaken the story is told of Benjamin
Franklin. He was not merely a first-class statesman but
he was also a very able research worker and discoverer
in natural science. At one time he took a great interest
in the problem of artificial manuring and clearly showed
the importance of its development in agrarian econom-
ics. He put his theories to the test and achieved practical
successes which were quite satisfying for his own scien-
tific bent of mind. But he found it very difficult to con-

THE ANSWER OF SCIENCE 149

vince his skeptical neighbors that the luxuriant crop of
clover which they saw growing in Franklin's field was
due to the use of artificial manure. For the peasant,
clover was clover and land was land and there were
good land and bad land and good weather conditions
and bad weather conditions, and these were the only
factors that he recognized as causes of a good crop or a
poor crop. Franklin determined to convince the peasant
that the art of man could directly influence the quality
of nature's growth. At the time of seed-sowing he dug
in the soil a series of small furrows which formed alpha-
betical letters. These small furrows he filled with rich
quantities of artificial manure, while the other parts of
the field were left solely to nature's hand. As the crop
grew the letters that corresponded to the manured fur-
rows showed rows of clover much taller and more lux-
uriant than that in the other parts of the field ; so that
the passers-by were able to read the sentence: This fart
has been manured with gypsum. History does not relate
whether the obstinate peasants were or were not con-
vinced by the proof. But that is neither here nor there ;
for nobody can be forced on purely logical grounds to
acknowledge the causal connection, because the causal
connection is not logically demonstrable. The point of
the illustration here is that if in a particular case we (
introduce a cause which of its very nature "flows into"
the result, as the scholastics used to say, and if the re-
sult is in full accord with what was predicted, then we
can be certain of the causal relation. In the instance of
Franklin's clover there could possibly be no other ex-

150 WHERE IS SCIENCE GOING?

planation except that of the manuring, and this
explanation, as a cause, has a natural and exclusive
connection with the result.

Of course it may be said that the law of causality is
only after all an hypothesis. If it be an hypothesis it is
not an hypothesis like most of the others, but it is a fun-
damental hypothesis because it is the postulate which is
necessary to give sense and meaning to the application of
all hypotheses in scientific research. This is because any
hypothesis which indicates a definite rule presupposes
the validity of the principle of causation.

We now come to those sciences which deal with hu-
man events. Here the method which the scientist follows
can have nothing like the same exactitude as that which
he follows in physics. The object of his study is the
human mind and its influence on the course of events.
The great difficulty here is the meager supply of source
materials. While the historian or the sociologist strives
to apply purely objective methods to his lines of investi-
gation, he finds himself confronted on all hands with
the want of data whereby he might determine the causes
that have led to general conditions in the past and lead
to the general conditions in the world at the present
moment. At the same time, however, he has at least one
advantage here which the physicist has not. The his-
torian or the sociologist is dealing with the same kind of
activities as he finds in himself. Subjective observation
of his own human nature furnishes him with at least a
rough means of estimation in dealing with outside per-
* sonalities or groups of personalities. He can "feel into"

THE ANSWER OF SCIENCE 151

them as it were and may thus gain a certain insight into
the characteristics of their motives and their thoughts.

Let us ask then what is the attitude of the humanist
scientist towards this problem of causation. In the activi-
ties of the human mind and in the play of human emo-
tions, and in the outer conduct that results from these,
is there everywhere a rigid causal interrelation? And is
all conduct in the last resort to be attributed to the causal
activity of circumstances, such as past events and present
surroundings, leaving no place whatsoever for an abso-
lutely spontaneous action of the human will? Or have
we here, in contradistinction to nature, at least a certain
degree of freedom or arbitrary volition or chance,
whichever name one wishes to choose? From time im-
memorial this question has been a source of controversy.
Those who hold that the human will is absolutely free
in its act of volition generally assert that the higher we
go in the scale of natural being the less noticeable is the
play of necessity and the greater the play of creative
freedom, until we finally come to the case of human be-
ings, who enjoy the full autonomy of the will.

Such an opinion cannot be spoken of as correct or
incorrect except by putting it to the test of historical
and psychological research. And here we have the prob-
lem in exactly the same position as in the case of physical
science. In other words we cannot know how far the I
principle of causality is valid except by putting it to the J
test of outer reality. Of course, a different terminology i
is used when causal methods are applied in the humanist
sciences. In natural science a definite physical picture

152 WHERE IS SCIENCE GOING?

with given characteristics is the subject of research. In
psychology we have a definite individual personality to
study. That individual personality has inherited quali-
ties such as bodily conformation, intelligence, imagina-
tive capacity, temperament, personal tastes and so on.
Working on this personality we have the physical and
psychic influences of the environment, such as climate,
food, upbringing, companionship, family life, education,
reading, etc. Now the question is whether all these data
determine the conduct of this personality in all its par-
ticulars and according to definite laws. In other words if
we suppose, what is impossible in practice, that we had a
thorough and detailed knowledge of all these factors
here and now, could we tell with certainty, on the causal
basis, how the individual will act a moment hence?

In seeking for a sound and logical and adequate
answer to this question we are here in quite a different
position from that in which we were when dealing with
natural science. Obviously it is extremely difficult to
give anything like a definite answer to such a question
as that asked above. One may have opinions and make
suppositions and assumptions ; but these do not furnish
logical grounds for an answer. Still I think that it
may be said definitely that the direction in which the
humanist sciences, such as psychology and history, are
developing nowadays furnishes certain grounds for pre-
suming that the question should be answered in the
affirmative. The part which force plays in nature, as
the cause of motion, has its counterpart in the mental
sphere in motive as the cause of conduct. Just as at

THE ANSWER OF SCIENCE 153

each and every moment the motion of a material body
results necessarily from the combined action of many
forces, so human conduct results with the same necessity
from the interplay of mutually reinforced or contra-
dicting motives, which partly in the conscious and par-
tially also in the unconscious sphere work their way
forward towards the result.

Of course it is perfectly true that many acts which
are done by human beings appear to be inexplicable.
At times it is an extraordinarily difficult riddle to find
anything like reasonable grounds for certain acts, and
other acts seem so utterly foolish as to suggest no
grounds at all. But consider for a moment the way
these acts appear to a trained psychologist and the way
they appear to the ordinary man in the street. What is
entirely puzzling to the latter is often quite clear to
the former. Therefore if we could study the acts of
the human being at very close and intimate quarters,
we should find that they can be accounted for through
causes which lie in the character or in the momentary
emotional tension or in the specific external environ-
ment. And in those cases where it is extremely difficult
and wellnigh impossible to discover these explanatory
causes, then we have at least grounds for assuming that
if we cannot find any motive as an explanation, we
must attribute this not actually to the absence of motive
but rather to the unsatisfactory nature of our knowl-
edge of the peculiarities of the situation. Here we have
the same case as in the throwing of the unsymmetrical
dice. We know that the way in which the dice finally

154 WHERE IS SCIENCE GOING?

comes to rest is the net result of all the factors active
in the throwing of the dice, but in the case of a single
throw we cannot detect the function of strict causality.
And so, even though the motive of a certain line of
human conduct may often lie utterly hidden, conduct
entirely without motive is scientifically just as incom-
patible with the principles on which mental science is
carried on as the assumption of absolute chance in inor-
ganic nature is incompatible with the working principle
of physical science.

It is not merely, however, that conduct is conditioned
by the motives which lead to it. Each act has also a
causal influence on subsequent behavior. And so in the
interchange of motive and conduct we have an endless
chain of events following one another in the spiritual
life, in which every link is bound by a strict causal re-
lation not only with the preceding link but also with
the following one.

Attempts have been made to find a way to free these
links from the causal chain. Hermann Lotze, in open
contradiction to Kant, put forward the suggestion that
such a causal chain can have no end, although it has a
beginning. In other words, that circumstances occur in
which motives appear entirely independently, not
caused by any preceding influence, so that the conduct
to which these motives lead will be the first link in
a new chain. Such an interpretation, Lotze held, must
be given especially to the acts of those choice spirits
that are called creative geniuses.

Even though we may not question the possibility of

THE ANSWER OF SCIENCE 155

such cases happening in the world of reality yet we may
reasonably answer that the thoroughgoing scientific re-
search which has been carried on in the region of psy-
chology would have pointed to such a possibility. But
as far as psychological research has gone there are no
indications which might furnish a starting-ground for
this theory of the so-called free beginning. On the
contrary, the deeper scientific research goes into the
peculiarities that have characterized even the great
spiritual movements of world history, more and more
the causal relation emerges into the open. The de-
pendence of each event upon preceding fact and pre-
paratory factors gradually begins to appear under the
strong light of scientific investigation, so much so as
to warrant the statement that present-day scientific
procedure in psychology is founded practically exclu-
sively on the principle of causal interrelations and the
assumption of an active law of causality which permits
no exceptions. This means that the postulate of com-
plete determinism is accepted as a necessary condition
for the progress of psychological research.

Under these circumstances it is obvious that we
cannot erect a definite boundary and say: Thus far but
no farther. The principle of causality must be held to
extend even to the highest achievements of the human
soul. We must admit that the mind of each one of
our greatest geniuses — Aristotle, Kant or Leonardo,
Goethe or Beethoven, Dante or Shakespeare — even at
the moment of its highest flights of thought or in the
most profound inner workings of the soul, was subject

156 WHERE IS SCIENCE GOING?

to the causal fiat and was an instrument in the hands of
an almighty law which governs the world.

The average reader may be easily taken aback by
such a statement. It may sound derogatory to speak
thus of the creative achievements of the highest and
noblest of the human race. But on the other hand it
must be remembered that we ourselves are only com-
mon mortals, and that we could never hope to be in
a position to follow out the delicate play of cause and
circumstance in the soul of the genius. There is nothing
derogatory in saying that they are subject to the law
of cause and effect, though it would be derogatory, of
course, if this were interpreted in the sense that the
ordinary mortal is capable of following the workings
of that law in the case of supremely gifted souls. No-
body would feel it disrespectful if one were to say that
some superhuman intelligence could understand a
Goethe or a Shakespeare. The whole point lies in the
inadequacy of the observer. Just so the macroscopic
physicist is entirely unable to pursue microscopic work-
ings in natural phenomena, yet, as we have seen, this
does not mean that the law of causality is not valid
for these microscopic happenings.

Where is the sense then, it may here be asked, in
talking of definite causal relations in regard to cases
wherein nobody in the world is capable of tracing their
function?

The answer to that question is simple enough. As
has been said again and again, the concept of causality
is something transcendental, which is quite independent

THE ANSWER OF SCIENCE 157

of the nature of the researcher, and it would be valid
even if there were no perceiving subject at all. We
shall see more clearly the inner meaning of the causal
concept if we consider the following: —

At this present moment of time and space the human
intellect as we know it may possibly not be the highest
type of intellect in existence. Higher intelligences may
exist in other places or may appear in other epochs.
And the intellectual level of these beings may be as
much above ours as ours is above the protozoa. Then
it may well happen that before the penetrating eye of
such intelligences even the most fleeting moment of
mortal thought, as well as the most delicate vibration
in the ganglia of the human brain, could be followed
in each case, and that the creative work of our mortal
geniuses could be proved by such an intelligence to
be subject to unalterable laws, just as the telescope of
the astronomer traces the links of the manifold move-
ment of the spheres.

Here, as everywhere else, we must differentiate be-
tween the validity of the causal principle and the prac-
ticability of its application. Under all circumstances the
law of causation is valid, because of its transcendental
character. But as its application can be carried out in
full detail only by the microscopic observer in natural
science, so in the region of the human mind the law
can be applied only by an intelligence that is far supe-
rior to the object of research. The smaller the distance
between the investigator and the object in this case, the
more uncertain and fallible will be the causal and sei-

i58 WHERE IS SCIENCE GOING?

entific treatment. The whole problem lies in the diffi-
culty, indeed the impossibility, with which we are faced
in trying to understand the behavior of a genius from
the standpoint of causation. Even a congenial spirit
in such cases would have to be content with presump-
tions and analogies j but to the average blockhead the
genius will ever remain a closed book signed with the
seven seals.

The conclusion, therefore, is that the highest types
of human intelligence are subject to the causal law
in the processes that result in even their greatest
achievements. That is the first part of our conclusion.
And the second part is that in principle we must reckon
with the possibility that a day will come when the more
profound and increasingly more refined development
of scientific research will be able to understand the
mental workings not only of the ordinary mortal but
also of the highest human genius in their causal rela-
tions; because scientific thought is identical with causal
thought, so much so that the last goal of every science
is the full and complete application of the causal prin-
ciple to the object of research.

From all that I have said what conclusion are we to
draw in regard to Free Will? In the midst of a world
where the principle of causation prevails universally,
what room is there for the autonomy of human voli-
tion? This is an important question, especially to-day,
because of a widespread tendency unwarrantably to
extend the tenets of scientific determinism to human
conduct and thus shelve responsibility from the shoul-

THE ANSWER OF SCIENCE 159

ders of the individual. We have had an example of
this in some modern interpreters of historical develop-
ment who would hold that the destiny of a group of
individuals, forming a nation or a civilization, is deter-
mined by blind fate. Therefore in the last analysis the
responsibility for such a destiny does not rest with the
individual. Is this attitude a legitimate deduction from
all that I have said? In other words, amid the all-
round causal sequence in natural phenomena is there
still room for the free and responsible act of the will
of the individual?

Before directly answering that question I may point
to a notable characteristic of everyday life which may
help us in forming a decision. Though chance and
miracle in the absolute sense are fundamentally ex-
cluded from science, yet science is confronted to-day,
more than ever before perhaps, with a widespread
belief in miracle and magic. Such belief, which has
been so universal in former ages, repeats itself with
the passing of the centuries in innumerable forms. This
means that science is repeatedly called upon to give the
scientific causal explanation of facts that are popularly
interpreted in the light of some belief. Belief in miracle
is a very important element in the cultural history of
the human race. It has brought untold blessings and
has inspired noble men to the greatest of heroic deeds.
But where it has degenerated into fanaticism it has
also been the cause of untold evil.

In view of the remarkable progress of physical
science during our own time and the universal exten-

i6o WHERE IS SCIENCE GOING?

sion of its benefits amongst civilized nations, we might
naturally assume that one of the achievements of
science would have been to restrict belief in miracle.
But it does not seem to do so. The tendency to believe
in the power of mysterious agencies is an outstanding
characteristic of our own day. This is shown in the
popularity of occultism and spiritualism and their in-
numerable variants. Though the extraordinary results
of science are so obvious that they cannot escape the
notice of even the most unobservant man in the street,
yet educated as well as uneducated people often turn
to the dim region of mystery for light on the ordinary
problems of life. One would imagine that they would
turn to science, and it is probably true that those who
do so are more intensely interested in science and are
perhaps greater in number than any corresponding
group of people in former times ; but still the fact
remains that the drawing power of systems which are
based on the irrational is at least as strong and as wide-
spread as ever before, if not more so. The Monist
League which was formed some years ago with so
much eclat and promise, for the purpose of establishing
a world outlook based on purely scientific grounds, has
certainly not achieved any success corresponding to the
rival systems.

How is this peculiar fact to be explained? Is there,
in the last analysis, some basically sound foothold for
this belief in miracle, no matter how bizarre and illogi-
cal may be the outer forms it takes? Is there something
in the nature of man, some inner realm, that science

THE ANSWER OF SCIENCE 161

cannot touch? Is it so that when we approach the inner
springs of human action science cannot have the last
word? Or, to speak more concretely, is there a point
at which the causal line of thought ceases and beyond
which science cannot go?

This brings us to the kernel of the problem in
regard to free will. And I think that the answer will
be found automatically suggested by the questions
which I have just asked.

The fact is that there is a point, one single point in
the immeasurable world of mind and matter, where
science and therefore every causal method of research
is inapplicable, not only on practical grounds but also
on logical grounds, and will always remain inapplicable.
This point is the individual ego. It is a small point in
the universal realm of being ; but in itself it is a whole
world, embracing our emotional life, our will and our
thought. This realm of the ego is at once the source '
of our deepest suffering and at the same time of our
highest happiness. Over this realm no outer power of
fate can ever have sway, and we lay aside our own
control and responsibility over ourselves only with the
laying aside of life itself.

And yet there is a way in which the causal method
can be applied within the limits of this inner realm.
In principle there is no reason whatsoever why the
individual should not make himself the observer of
what has happened within himself. In other words, he
can look back over the experiences through which he
has passed and endeavor to link them up in their causal

i62 WHERE IS SCIENCE GOING?

relations. There is no reason indeed, at least in prin-
ciple, why he should not scrutinize each experience —
by which I mean each decision and line of conduct
which he has taken — and study it from the viewpoint
of finding out the cause from which it resulted. Of
course that is an extremely difficult task; but it is the
only soundly scientific way of dealing with our own
lives. In order to carry out this plan of action the facts
of our own lives which we now place under observation
would have to be distanced in the past, so that our
present complex of living emotions and inclinations
would not enter as factors into the observation. If we
could possibly carry out the plan in this detached way,
then each experience through which we have passed
would make us immeasurably more intelligent than we
were before, so intelligent indeed that in relation to our
earlier condition we should rise to the level of the
super-intelligence postulated by Laplace. You remem-
ber that Laplace held that if there were a super-
intelligence standing entirely outside of the facts
occurring in the universe, this intelligence would be
able to see causal relations in all the happenings of the
world of man and nature, even the most intricate and
microscopic. It is only by aiming at this sort of distance
that the individual could establish the required detach-
ment of the perceiving subject from the object of his
research, which we have already seen to be an inevitable
condition for the application of the causal method in
research. The nearer we are to events in time the more
difficult it is to trace their causal structure. And the

THE ANSWER OF SCIENCE 163

nearer we are to the events of our own personal experi-
ence the more difficult it is for us to study ourselves
in the light of these happenings; for the activities of
the observer are here partly the object of research and,
in so far as that is so, the causal connection is prac-
tically impossible to establish. I am not preaching a
moral sermon here or suggesting what ought to be
aimed at for the sake of the moral uplift of one's own
being. I am only treating the case of individual free-
dom from the viewpoint of its logical coherence with
the principle of causation, and I am saying that in
frincifle there is no reason why we should not discover
the causal connections in our own personal conduct,
but that in practice we never can do so because this
would mean that the observing subject would also be
the object of research. And that is impossible; for no
eye can see itself. But in so far as any man is not
entirely to-day that which he was years ago there is
a relative degree to which he might subject his own
experiences to causal scrutiny; and I have mentioned
this as illustrative of the general principle.

It will occur to many readers to ask if thus in rela-
tion to the chain of causality the freedom of the indi-
vidual will, here and now, is only apparent and results
solely from the defects of our own understanding. That
way of putting the case is, I am convinced, entirely mis-
taken. We might illustrate the mistake by saying that
it is like the mistake of suggesting that the inability of
a runner to outrun his own shadow is due to his lack
of speed. The fact that the individual here and now,

i64 WHERE IS SCIENCE GOING?

in regard to his own living present act, cannot be sub-
ject to the law of causation is a truth that is based on
a perfectly sound logical foundation of an a friori
kind, such as the axiom that the part is never greater
than the whole. The impossibility of the individual con-
templating his own activity here and now under the
light of the causal principle would hold good even in
the case of the super-intelligence postulated by Laplace.
For, even though this super-intelligence might be able
to trace the causal structure in the achievements of the
most gifted geniuses of the human race, yet that same
super-intelligence would have to renounce the idea of
studying the activities of its own ego at the moment it
contemplated the activities of our mortal ego. If there
be a Supreme Wisdom whose celestial nature is in-
finitely elevated above ours, and who can see every
convolution in our brains and hear every pulse beat of
each human heart, as a matter of course such a Supreme
Wisdom sees the succession of cause and effect in every-
thing we do. But this does not in the least invalidate
our own sense of responsibility for our own actions.
From this standpoint we are on an equal footing with
the saints and confessors of the most sublime religions.
We cannot possibly study ourselves at the moment or
within the environment of any given activity. Here
is the place where the freedom of the will comes in
and establishes itself, without usurping the right of
any rival. Being emancipated thus, we are at liberty
to construct any miraculous background that we like
in the mysterious realm of our own inner being, even

THE ANSWER OF SCIENCE 165

though we may be at the same time the strictest
scientists in the world, and the strictest upholders of
the principle of causal determinism. It is from this
autarchy of the ego that the belief in miracles arises,
and it is to this source that we are to attribute the
widespread belief in irrational explanations of life. The
existence of that belief in the face of scientific advance
is a proof of the inviolability of the ego by the law of
causation in the sense which I have mentioned. I might
put the matter in another way and say that the freedom
of the ego here and now, and its independence of the
causal chain, is a truth that comes from the immediate
dictate of the human consciousness.

And what holds good for the present moment of
our being holds good also for our own future conduct
in which the influences of our present ego plays a part.
The road to the future always starts in the present.
It is, here and now, part and parcel of the ego. And
for that reason the individual can never consider his
own future purely and exclusively from the causal
standpoint. That is the reason why fancy plays such a
part in the construction of the future. It is in actual
recognition of this profound fact that people have re-
course to the palmist and the clairvoyant to satisfy
their individual curiosity about their own future. It is
also on this fact that dreams and ideals are based, and
here the human being finds one of the richest sources
of inspiration.

I might mention here in passing that this practical
inapplicability of the law of causation extends beyond

i66 WHERE IS SCIENCE GOING?

the individual. It extends to our relations with our
fellow-men. We are too much a part of the life of
our fellow beings to be in a position to study them
from the viewpoint of motives, which means the causal
viewpoint. No ordinary human being can put himself
in the position of the super-intelligence imagined by
Laplace and consider himself capable of tracing all the
inner springs of action from which the conduct of his
fellow-men originates. On the other hand, however, I
would mention here again a phase of the causal appli-
cation corresponding to that which I have already
spoken of in relation to the individual's capacity for
scientifically observing his own past experience. To a
relative degree it is possible to study the motives on
which other people act, just as they are studied by the
psychologist or the alienist. In all such cases there is
to a certain degree the requisite distance between the
researcher and the object of his research. And therefore
to this extent there is no logical incoherence in the idea
of a person studying Jthe activities of his fellow beings.
Indeed all who wish to influence others do so in every-
day life, which is largely the secret of political suc-
cess. It is the secret of all the power for good which
so many people exercise in relation to their fellow
beings. Most of us remember from childhood per-
sonalities whom we shirked because of some sort of
innate feeling of insecurity in their presence, and on
the other hand most of us, I imagine, have memories
of acquaintances to whose influence we were willingly
amenable because we felt a certain reverence towards

THE ANSWER OF SCIENCE 167

s

them. And everybody is more or less familiar with the ^
feeling of withdrawal which comes over one in the
presence of a person who is suspected of seeing too
clearly into the inner lives of others. All these imme-
diate reactions bear witness to a sort of instinctive
recognition that our own lives are in the last analysis
subject to causation, though the ego as regards its
immediate destiny cannot be subject to that law.

Science thus brings us to the threshold of the ego
and there leaves us to ourselves. Here it resigns us to
the care of other hands. In the conduct of our own
lives the causal principle is of little help; for by the j
iron law of logical consistency we are excluded fromj
laying the causal foundations of our own future or
foreseeing that future as definitely resulting from the \
present.

But mankind has need of fundamental postulates
for the conduct of everyday existence, and this need
is far more pressing than the hunger for scientific
knowledge. A single deed often has far more signifi-
cance for a human being than all the wisdom of the
world put together. And therefore there must be an- '
other source of guidance than mere intellectual equip-
ment. The law of causation is the guiding rule of
science; but the Categorical Imperative — that is to say,
the dictate of duty — is the guiding rule of life. Here
intelligence has to give place to character, and scientific
knowledge to religious belief. And when I say religious
belief here I mean the word in its fundamental sense.
And the mention of it brings us to that much discussed

i68 WHERE IS SCIENCE GOING?

question of the relation between science and religion.
It is not my place here nor within my competency to
deal with that question. Religion belongs to that realm
that is inviolable before the law of causation and there-
fore closed to science. The scientist as such must recog-
nize the value of religion as such, no matter what may
be its forms, so long as it does not make the mistake of
opposing its own dogmas to the fundamental law upon
which scientific research is based, namely, the sequence
of cause and effect in all external phenomena. In con-
junction with the question of the relations between
religion and science, I might also say that those forms
of religion which have a nihilist attitude to life are
out of harmony with the scientific outlook and con-
tradictory to its principles. All denial of life's value
for itself and for its own sake is a denial of the world
of human thought, and therefore in the last analysis
a denial of the true foundation not only of science
but also of religion. I think that most scientists would
agree to this, and would raise their hands against
religious nihilism as destructive of science itself.

There can never be any real opposition between
religion and science -y for the one is the complement
of the other. Every serious and reflective person
realizes, I think, that the religious element in his na-
ture must be recognized and cultivated if all the
powers of the human soul are to act together in perfect
balance and harmony. And indeed it was not by any
accident that the greatest thinkers of all ages were
also deeply religious souls, even though they made no

THE ANSWER OF SCIENCE 169

public show of their religious feeling. It is from the $
cooperation of the understanding with the will that /
the finest fruit of philosophy has arisen, namely, the
ethical fruit. Science enhances the moral values of life,
because it furthers a love of truth and reverence — *
love of truth displaying itself in the constant endeavor
to arrive at a more exact knowledge of the world of
mind and matter around us, and reverence, because
every advance in knowledge brings us face to face
with the mystery of our own being.

CHAPTER VI

FROM THE RELATIVE TO THE
ABSOLUTE

1HOPE the reader will not be frightened away by
the sound of this title. I should have chosen
another terminology if I could have found one better
suited to my purpose. But the above title is the most
expressive I can find to indicate an outstanding feature
of scientific development which I wish to describe
here. This feature has been remarkably characteristic
of physical science during the past hundred years. The
line of progress has been from the relative to the
absolute. We need not delay here to discuss the various
meanings given to these words in scientific and semi-
scientific parlance nowadays. I am using them as the
man in the street uses them in everyday life. And the
meaning in which we are to take them here will best
be made clear by getting directly into touch with the
facts to which that meaning is applicable.

Let us begin with the discussion of one of the most
elementary concepts in chemistry — atomic weights. The
idea of the atom itself dates from the time of the
Grecian philosophers. And indeed the word itself, in
Greek, means that which cannot be divided. The art of

170

FROM RELATIVE TO ABSOLUTE 171

measuring atomic weights, however, dates from the dis-
covery of a fundamental principle in stoechiometry.
Stoechiometry, by the way, is another Greek word. It
is the name which is given to the science of estimating
chemical elements. Now, the stoechiometrical principle
to which I have just referred is that all chemical com-
pounds result from definite ratios between the weight
of one element and another in the compound. For
instance, one gram of hydrogen unites with eight grams
of oxygen to form water. And if one gram of hydro-
gen be united with 35.5 grams of chlorine the resulting
compound will be hydrochloric acid. If we take one
gram of hydrogen as the unit of measurement, we
say that eight grams is the equivalent weight of oxygen
and 35.5 grams the equivalent weight of chlorine. And
so for every chemical element in every compound
which it can form with another element we can ascertain
its equivalent weight. Of course the measurement is
based on the choice of hydrogen as a unit, and in that
sense of measurement it is somewhat arbitrary. That is
not all, however. Its validity is restricted to those spe-
cial elements with which hydrogen combines in order
to form a compound. The equivalent weight of oxygen
as 8 is valid only in its relation to water. If instead of
water we take hydrogen peroxide then the equivalent
weight of the oxygen will be 16. In principle there are
no grounds whatsoever for preferring one of these
numbers to the other. Every element therefore, gen-
erally speaking, has a varying equivalent weight. In
principle it has as many equivalent weights as there

172 WHERE IS SCIENCE GOING?

are combinations into which it can enter. If there be an
element which does not enter into any known combina-
tion then there is no term of reference whereby its
equivalent weight can be established. Now the inter-
esting fact is that in the different combinations into
which an element may enter with other elements to
form a compound, the elements will always be in rela-
tion to one another according to their equivalent weight
numbers, or a simple multiple of these. This is called
the law of multiple proportions, and it states that when-
ever two elements combine in more proportions than
one, the quantities of A, let us say, which combine
with a definite quantity of B are connected by a simple
multiple. Thus a quantity of chlorine having the
equivalent weight of 35.5 combines not only with one
gram of hydrogen, to form hydrochloric acid, but also
with eight grams of oxygen, to form chloroxide, while
it combines with one gram of hydrogen to form hydro-
chloric acid. Therefore there are key numbers which
can always be used to describe the proportions of vari-
ous elements present in the various compounds. To put
the matter in a plainer way, in every compound sub-
stance the proportional weight of each element may be
represented by a fixed number, or by this number mul-
tiplied by two, three, four or five and so on. Unless we
are to attribute to some inconceivable law of chance this
extraordinarily simple and regular scheme into which
the various compound substances fit perfectly, we must
admit that the idea of equivalent weight must be con-
sidered as having an independent significance, irrespec-

FROM RELATIVE TO ABSOLUTE 173

tive of the combination which the element can make
with other elements. Therefore in a certain sense this
equivalent weight must be looked upon as something
Absolute.

This is what happens in the actual world of fact.
But a difficulty which remained for a long time in-
soluble in chemistry arose from the fact that some
elements are not constant in their valency but may com-
bine with other elements in different ratios, such as
hydrogen with oxygen, so that one might take either
8 or 16 as indicating the equivalent weight of oxygen.
This difficulty could not be overcome until a new idea
was introduced which was foreign to stoechiometry.
This idea is contained in Avogadro's Law, which was
founded on facts discovered by Gay-Lussac, namely,
that two elements in a gaseous state combine with one
another not only in definite weight ratios but also in
definite volume ratios under equal pressure and tem-
perature. Avogadro's Law states that equal volumes of
different gases at the same temperature and pressure
contain the same number of molecules, that is to say,
the volume of a gram molecule is constant for all
gases. Therefore, from the many equivalent weights
which might be assigned to each element it was pos-
sible to select one definite weight, which was called the
molecular weight ; because the molecular weight of two
gases was found to be in constant ratio to their densities.
Here there was no longer any question of chemical
reaction but only of chemical substances. Therefore the
rule could be applied to elements such as perfect gas,

174 WHERE IS SCIENCE GOING?

which it is difficult or impossible to combine with other
substances.

According to the Avogadrian Law the molecules of
chemical elements often enter into the molecules of
the combination not with their whole weight but only
with a fraction of it. For instance, the molecule of
steam is made up of one whole molecule of hydrogen
and half a molecule of oxygen, whereas the molecule
of hydrochloric acid is made up of half a molecule
of chlorine and half a molecule of hydrogen. Therefore
from the molecular weight we come to the atomic
weight of an element as the smallest fraction which is
found in a combination of elements. This atomic weight
expresses the relative weights of each species of matter.

Although in Avogadro's Law the concept of atomic
weight has a certain absolute significance, at the same
time it has quite a relative connotation. The Avogadrian
atomic weight is only a relative number. Therefore
it cannot be determined except by an arbitrary refer-
ence to the atomic weight of some special element or
other, such as Hydrogen = i or Oxygen = 1 6. With-
out reference to some such given term, the number
describing the atomic weight would have no meaning.
Therefore it has for a long time been the aim of
chemical researchers to free the concept of atomic
weight from this restriction and try to give it a wider
and more absolute meaning. This problem, however, is
not very important for the practical chemist ; because
in the chemical analysis of substances there is always

FROM RELATIVE TO ABSOLUTE 175

the question of relative proportions among the com-
bining elements.

In every science it occasionally happens that there
arises a conflict between two classes of people whom I
may designate respectively as purists and pragmatists.
The former strive always after a perfect coordination
of the accepted axioms of their science, submitting them
to an ever more and more rigid analysis, for the pur-
pose of eliminating every contingent and foreign ele-
ment. On the other hand, the pragmatists try to amplify
the accepted first principles by the introduction of new
ideas and thus send out feelers in all directions for
the purpose of making progress. They do not mind if
the mongrel be mated with the pure-bred, provided
something can be achieved through the combination,
which otherwise could not be achieved. In the science
of chemistry also there are purists who set themselves
against any attempt to make the concept of atomic
weight something more than that of a merely relative
number. But there are also leading chemists who find
it at least practical to treat the atomic idea as it is
treated in mechanical physics, that is to say, to con-
sider the atoms as minute and independent particles
occupying definite and measurable dimensions in the
molecule, and being either divided or regrouped ac-
cording as the molecule undergoes chemical changes.
During my time in Munich, in the beginning of the
eighties, I remember being very much impressed by the
polemic that then raged in the university laboratory.
Among the puritan chemists the leader was then

176 WHERE IS SCIENCE GOING?

Hermann Kolbe of Leipzig, who hurled his sacred
anathema against the mechanical-atomic interpretation :
which was involved in the building up of chemical
formulas for the constitution of various substances.
When results were somewhat slow in being obtained by
that process he generally grew all the more violent
against the principle adopted. In the circumstances
von Baeyer did the wisest thing that could be done. 1
He kept silent and awaited results, until finally success
crowned his efforts.

A similar condition of affairs was reproduced re- 1
cently when the controversy arose over the atom model
suggested by Niels Bohr, which indeed demands a far
greater concession on the part of orthodox theorists!
than the earlier hypothesis of the atomic structure of
chemical elements.

On the philosophical side also there are purists who
have maintained a long-standing attitude of opposition!
to the atomic theory. Ernst Mach was the most out- 1
standing leader of this school. During his life he never
seemed to tire of using the weapon of conceptual;
analysis, and occasionally also his irony, for the pur-
pose of discrediting the rather naive and rudimentary
views of those who then championed the atomic prin-;
ciple. He believed that the revival of the old atomic
doctrine and the dressing of it in modern form signified
a retrogression, and hindered rather than helped the
philosophical development of modern physics.

Ludwig Boltzmann, as leading representative of the
atomic physicists, boldly endeavored to hold his ground

I

FROM RELATIVE TO ABSOLUTE 177

against Mach ; but the contest was rather difficult from
his side, because the purist sticks to his logical weapons.
He takes his stand on logical deductions from the ac-
cepted principles of science, whereas the pragmatist
scientist is striking out into new ground ; and in order
to open that up he must break away from the logical
line of the old ideas. The pragmatist must face failure
again and again, and is always open to the jibes of the
orthodox "I told you so." What the puritan objects
to is the introduction of new ideas and theorems from
outer sources, especially while those are in the stage
of not having produced any results in practice. Now, no
theorem or working hypothesis can arise ready-made,
like Pallas Athene from the head of Jupiter. Every
hypothesis which eventually has proved to be useful
and to have led to valuable discoveries at first occurred
only vaguely to the mind of its inventor. When Archi-
medes jumped out of his bath one morning and cried
Eureka he obviously had not worked out the whole
principle on which the specific gravity of various bodies
could be determined 5 and undoubtedly there were
people who laughed at his first attempts. That is per-
haps why most scientific pioneers are so slow to disclose
the nature of their first insights when they believe
themselves to be on a track of a new discovery. They
would have to stand against the massed batteries of
the purists, which would not be a very advisable posi-
tion for any one to take up who has to follow the
lead of his own instinct painfully and painstakingly
and refuse to be discouraged when his attempts end in

178 WHERE IS SCIENCE GOING?

failure. For every hypothesis in physical science has
to go through a period of difficult gestation and par-
turition before it can be brought out into the light of
day and handed to others, ready-made in scientific
form so that it will be, as it were, fool-proof in the
hands of outsiders who wish to apply it.

Even when a scientific theory has established its
right to existence by reason of the results it has pro-
duced, the purist often takes a long time to come
round. And that is because the success of a new theory
in physics cannot be decided according to its logical
consistency with accepted notions, but rather by the
test whether or not it explains and coordinates certain
facts already ascertained, but which cannot be explained
on any other grounds except that of the new hypothesis.
Of course the purists have always the old refuge to
fall back upon. They appeal to the element of chance.
And on that stand some of them will remain, while
others will take up an intermediate position of qualifie 1
skepticism j but the pragmatist finds that the hypothesis
in question has worked out a clear solution of certain
puzzles and he accepts it for what it does. Instead o
looking backwards he begins to look forward with
view to finding whether the hypothesis may not be
applied in other directions also. It was thus with th
fate of the quantum hypothesis, for instance. It was
originally formulated to explain a puzzle of radiation
which had long existed 5 but in the hands of Einstei
it was soon applied to explain the constitution of ligh

FROM RELATIVE TO ABSOLUTE 179

and, in the hands of Niels Bohr, to explain the structure
of the atom.

It was just in this way that the existence of an abso-
lute atomic weight came to be finally established. Here
I need not go into details to tell how so many lines of
research led finally to the discovery of the absolute
atomic weight. Among these many lines I may men-
tion the development of the kinetic theory for gases
and fluids, the laws governing the radiation of heat
and light, the discovery of the cathode rays and radio-
activity, and the measurement of the elementary elec-
trical quantum. To-day no physicist would question the
fact that the weight of an atom of hydrogen, setting
aside the unavoidable errors of measurement, amounts
to 1.649 quadrillionths of a gram. The value of this
number is entirely independent of the atomic weight
of other chemical elements, and in this sense it can
be called an absolute quantity.

All this of course is already a matter of common
knowledge. And I have mentioned it here in order to
illustrate a characteristic feature in the development
of scientific research. This phenomenon shows itself
under the most varied circumstances. Axioms are in-
struments which are used in every department of sci-
ence, and in every department there are purists who
are inclined to oppose with all their might any expan-
sion of the accepted axioms beyond the boundary of
their logical application.

I shall now suggest another case for consideration.
But this is by no means so simple as that which I have

i8o WHERE IS SCIENCE GOING?

already treated. In fact it is still the center of con-
tention.

Let us begin with a concept of energy. The term
"energy" represents the work that can be done by
forces acting on matter. And the Principle of the Con-
servation of Energy, which was formulated in the
middle of last century, was a development from the
concept of force in Newtonian mechanics. According to
the Principle of the Conservation of Energy, in every
mechanical process the amount of energy which the
moving force puts into the body moved is compensatec
for by a loss of potential energy on the part of the
acting force. Two kinds of energy were thus recog-
nized, namely potential energy and kinetic energy, the
former being the energy possessed by bodies at rest
and the latter being the energy of moving bodies.
There is no such thing then as absolutely lost energy,
but only a change from one kind of energy to another.
And the loss sustained by one kind of energy, the
potential, is compensated for by the gain in the other
kind of energy, the kinetic. In this connection the
purist might reasonably maintain that the formulation
of the Principle of the Conservation of Energy is valic
only for a difference of energy, and that the concept
of energy does not refer to the state of a body or, as
we say in scientific language, the state of a physica
system, but rather to a change in that state. Therefore
the energy value remains an indefinite superaddec
factor. And the question of its measurement would have
no meaning in physical science. It would have the same

I

FROM RELATIVE TO ABSOLUTE 181

relation to the physicist as the altitude above sea-level
would have for the architect who is building a house.
It is not the latter's business to bother himself about
this altitude. He has to confine himself to the altitude
of the house itself and that of the various floors of
which it is composed. Such is the objection that a purist
might urge.

His standpoint would be quite sound if the Principle
of the Conservation of Energy were the only axiom
employed in physical science. But this is not the case.
And therefore we cannot reject offhand the suggestion
that it may be well to introduce into the concept of
energy that of another axiom, if the result would be
that the state of a physical picture here and now could
thus be fully determined. If we could do that then it
is obvious that the concept of energy would be very
much simplified by the addition of something else to
the Principle of Conservation. As a matter of fact
that is what has been done to-day. For any physical
system in a given state we can find a definite expres-
sion for the magnitude of its energy, without any
superadded factor whatsoever.

Let us first take electromagnetic energy in a vacuum.
Here there is an axiom which establishes the absolute
value of that energy. It states that the energy of an
electromagnetic neutral field is equal to Zero. This
law is neither obvious in itself nor can it be deduced
from the Principle of the Conservation of Energy.
Only a few years ago Nernst formulated the hypoth-
esis that in the so-called neutral field there is a certain

i82 WHERE IS SCIENCE GOING?

stationary energy radiation of tremendous magnitude.
This is called the radiation of the Zero point. It can-
not be detected in the observation of ordinary processes
because it streams through all bodies equally, just as
the pressure of the atmosphere represents a very im-
portant force which plays no part in most of the
movements that we observe, because the pressure is
equal in all directions. Such a radiation hypothesis is
perfectly reasonable, and validity can be decided upon
only by the question of what results follow from its
application. For this application, however, it is abso-
lutely necessary to furnish a special reference system
that is immobile, namely that in which the Zero radia-
tion is equal in all directions. Through the absolute
energy of the neutral field the absolute energy of every
other electromagnetic field is thereby established.

Coming now to the energy of matter, for this we
can also obtain a definite absolute value. But the energy
of a body at rest is not equal to Zero as might prob-
ably be imagined, following the analogy of the electro-
magnetic neutral field. The energy of a body at rest
is equal to its mass multiplied by the square of the
velocity of light. This is the so-called rest energy of
the body, and is caused by its mechanical constitution
and its temperature. If the body be set in motion by
some force this energy value, which is of an enormous
amount, does not make itself felt because the phe-
nomenon of motion here arises from only a differen-
tiation of energy. Such a conception could never have
arisen from the energy principle itself. As a matter of

FROM RELATIVE TO ABSOLUTE 183

fact it arises from the special theory of relativity, and
it is a remarkable coincidence that it is just the theory
of relativity which has led to the determination of an
absolute value for the energy of a physical system.
This apparent paradox is explained by the simple fact
that in the relativity theory there is the question of
dependence on the reference system selected, whereas
here there is the question of dependence on the physical
state of the body under observation.

"Doesn't it in reality sound quite nonsensical to say
that the energy of an atom of oxygen is sixteen times
greater than that of an atom of hydrogen?" the purist
might ask. We might answer that there would be no
sense in such a statement if we could not speak of the
hypothetical transformation of oxygen into hydrogen
without involving a logical contradiction in the thought
itself. But the idea of oxygen being one day changed
into hydrogen does not involve any logical contradic-
tion. Now, it is a mistake in these matters to speak of
something as nonsensical unless it can be shown to be
logically incoherent ; and it would therefore seem more
advisable to wait and see whether a day may not come
when the problem of this transformation of oxygen
into hydrogen may assume a reasonable significance.
There are already signs that this time is at hand.

As in the case of electromagnetic and kinetic energy
so, too, in all departments of physics, mechanics as well
as electrodynamics, the movement has been away from
dealing with differentials of energy towards dealing
with absolute values of it. And this direction has in-

i84 WHERE IS SCIENCE GOING?

variably led to important results. When considering the
phenomenon of heat radiation, for instance, it was
always the strict rule to deal only with the difference
between the radiation absorbed and that emitted 5 be-
cause all the heat rays that a body absorbs it can also
give out. But in the theory of Prevost these two proc-
esses were separated from one another and each of
them given an independent meaning. In galvanism
only the potential difference was measured ; but the
absolute value of the potential was also recognized
because the potential energy of all electric charges
at infinite distances was declared to be equal to Zero.
For the emission of monochromatic radiation in the
case of an atom the measurement of the frequency
emitted gave only a difference of the atomic energy
before and after the emission. But by first separating
the two factors of this difference — the so-called terms
— and then examining each separately, Niels Bohr and
Arnold Sommerfeld were able to discover a clew for
the solution of the mystery, Niels Bohr in the case
of visible rays and Arnold Sommerfeld for the
Roentgen rays.

It is not, however, merely in its dealings with the
problem of energy that progress from the differential
to the integral is characteristic of physical science. We
find the same feature showing itself in every other
branch of physical research. Thus the older elasticity
theory of body force is now referred back to sur-
face forces. In electrodynamics electric and magnetic
penderometer forces are resolved into the so-called

PROM RELATIVE TO ABSOLUTE 185

Maxwellian tension. The thermodynamic measure-
ments of temperature and pressure are resolved into
the thermodynamical potential. In each of these cases
the progress signifies a new stage in the evolution of
theoretical physics.

But there is one evolutionary struggle going on
which deserves a little more detailed notice because it
is still in an undecided phase. It is the problem of
trying to find an absolute value for entropy. In the
original definition of entropy put forward by Rudolf
Clausius, if we are to measure the entropy of a body
there must be a reversible process of some kind to
enable us to determine the difference of entropy be-
tween the initial state and the final state of the process.
In the light of this theory the concept of entropy
originally referred not to a state but rather to a change
of state, exactly as was the case in regard to atomic
weight and energy. Indeed, the earlier scientific notion
was that the concept of entropy had a physical signifi-
cance only where there could be a reversible process.
It did not take long, however, before a broader con-
cept was put forward and entropy began to be looked
upon as a characteristic or inherent quality in the state
of a body here and now. In this new way of looking
at the case, however, there still remained an undefined
additive constant, because one could still measure only
the difference of entropy. Were we to follow the lead
suggested by the Einstein experiments, and base the
concept of entropy on the statistical laws governing the
oscillations of a physical picture in relation to its

i86 WHERE IS SCIENCE GOING?

thermodynamic state of equilibrium, even then we
should only arrive at a measurement of differences,
involved in a change of entropy, but never at the
absolute value of entropy itself.

Is there then any way whereby we can hope to find
an absolute value for entropy as has been found for
energy? I do not think that the question can be an-
swered on the basis of an analogy between these two
cases. When such suggestions come to the fore I am
always inclined to take my stand with the purists, who
hold that it is senseless to try to arrive at the values
of both termini from the value of the difference. If
we are to keep our outlook clear we must always be
very careful as to what can or cannot be deduced from
a definition. In this regard the criterion of the purists
is indispensable. We must do them the honor of saying
that they are the conscientious wardens of order and
purity in scientific methods. There is nothing more
seductively dangerous in scientific work than the intro-
duction of extraneous analogies into the problem at
issue. That is a warning which needs to be sounded
to-day even more insistently than before. But at the
same time we must bear in mind the fact that physics
is not a deductive science, and that its body of first
principles is by no means fixed and unalterable. If a
new axiom be suggested which we might introduce,
then instead of rejecting it at once it ought to be put
into quarantine, as one might say, and examined on
its own merits for a clean bill of health. That clean
bill of health which will give it a right to citizenship

FROM RELATIVE TO ABSOLUTE 187

in physical science must be drawn up entirely free from
prejudice as to the alien status of the axiom. The claim
of the axiom must be adjudicated on the grounds of
its ability to serve the cause of science in some direction
where service is needed, and where the native axioms
are unable to discharge such service. Once the new
axiom has shown that it can solve hitherto insoluble
problems, or at least produce a working hypothesis for
their explanations, then it has a perfect right to be
admitted.

Before indicating a definite line along which the
question I have given above may eventually be an-
swered, I will call attention to the difference between
reversible and irreversible processes, as from this we
shall understand the Boltzmann hypothesis which
would suggest the answer. Suppose we take a piece
of iron heated to a very high temperature and plunge
it into a vessel of cold water. The heat of the iron
will pass to the water until both iron and water are
of an equal temperature. This is called thermal equi-
librium, which results after all such cases of disturbance
if there be nothing to prevent the conduction of the
heat.

Now let us take two vertical tubes of glass which are
open at the upper ends and have the lower ends con-
nected by a piece of rubber tubing. If we pour some
heavy liquid such as mercury into one of the glass
tubes the liquid will flow through the rubber into the
second tube and rise in it until the level of the surfaces
on both tubes is the same. Now supposing we lift one

188 WHERE IS SCIENCE GOING?

of the tubes somewhat, the level is disturbed 5 but the
fluid will fall back immediately when we replace the
tube and will again be the same height in both. Between
this instance and that of the bar of iron in the vessel
of water there is a certain analogy. In each case a certain
difference brings about a change. In the case of the tube
which we raise a little higher than the other there is a
change of level, and in the case of the iron and water
there is at the moment of immersion a difference be-
tween the temperatures. If in each case we allow the
total mass to rest sufficiently long the differences will
disappear and a condition of equilibrium will result.

As a matter of fact the analogy between these two
cases is only apparent. All experiments which have
been made warrant us in definitely asserting that the
action of the liquid in the tubes follows a dynamical
law, but that the energy of temperature follows a
statistical law.

To understand this apparent paradox we must re-
member that the sinking of the heavy liquid is a neces-
sary consequence of the Principle of Conservation of
Energy. For if the liquid at a higher level were to rise
still higher irrespective of any external agency, and the
liquid of the lower level to sink still lower, energy
would be created out of nothing. That is to say, new
energy would appear and thus be entirely contrary to
the principle. The temperature case is different. Heat
could flow in the reverse process from cold water to hot
iron, and the Principle of Conservation of Energy still
hold good 3 because heat itself is a form of energy, and

FROM RELATIVE TO ABSOLUTE 189

the principle only demands that the quantity of heat
given up by water be equal to that absorbed by the iron.

Now the two operations show the following different
characteristics. The falling liquid moves faster the fur-
ther it falls. When the level in one tube corresponds
to the level in the other the liquid does not come to
rest, but moves beyond the equilibrium point on account
of its inertia, so that the liquid originally at the higher
level is now at a lower level than that rising in the
corresponding tube. The velocity of the falling liquid
will gradually sink to zero in tube No. 1 and then the
reverse process sets in, that is to say, the lowering of the
level in tube No. 2. If loss of kinetic energy at the air
surface, and that due to friction at the walls of the tube
could be eliminated, the liquid would oscillate upwards
and downwards indefinitely over and under its position
of equilibrium. Such a process is called reversible.

Now in the case of heat the condition is quite other-
wise. The smaller the difference of temperature between
the hot iron and the water the slower is the transmission
of heat from the one to the other, and calculation shows
that an infinitely long time passes before an equal tem-
perature is reached. This means that there is always
some difference of temperature no matter how much
time be allowed to elapse. There is no oscillation of
heat therefore between two bodies. The flow is always
in one direction and therefore represents an irreversible
process.

This difference between reversible and irreversible
processes is fundamental in physical science. Reversible

190 WHERE IS SCIENCE GOING?

processes include gravitation, mechanical and electrical
oscillations, sound waves and electromagnetic waves
Irreversible processes are found in the conduction of
heat and electricity, radiation and all chemical reactions
in so far as the velocity is ascertainable. It was to explain
this case that Clausius formulated his second law of
thermodynamics. The significance of the law is that it
ascribes direction to each irreversible process. It was L.
Boltzmann, however, who introduced the atomic theory
here and thus explained the meaning of the second law,
and at the same time of all irreversible processes which
hitherto had presented difficulties that could not be ex-
plained in classical dynamics.

According to this atomic theory the thermal energy
of a body is the sum-total of a small, rapid, and un-
regulated movement of its molecules. The temperature
corresponds to the medium kinetic energy of the mole-
cules, and the transfer of heat from a hotter to a colder
body depends upon the fact that the kinetic energies of
the molecules are averaged because of their frequent
collision with one another. It must not be supposed, how-
ever, that when two individual molecules strike together
the one with the greater kinetic energy is slowed down
and the other accelerated, for if — to take an example —
a rapidly moving molecule of one system is struck
obliquely by a slower moving molecule its velocity is
increased while that of the slower moving molecule
is still further diminished. But, taken on the whole,
unless the circumstances are quite exceptional the kinetic
energies must mix to a certain amount, and this mixing

FROM RELATIVE TO ABSOLUTE 191

is what appears as an equalizing of the temperature of
the two bodies.

Boltzmann, however, did not press his hypothesis very
strongly before the notice of scientists and there was
great hesitancy about accepting it, but nowadays it is
fully accepted. It is now generally agreed that heat
movement of molecules and conduction of heat, like
all other irreversible phenomena, does not obey dy-
namical laws but statistical laws. The latter are the laws
of probability.

Now in the case under consideration it is not at all
difficult to say what the idea is that lies behind the
assumption of an absolute value for entropy. And if
a new axiom can serve that idea we ought to admit it.
As to the idea of absolute value for entropy, if we
follow Boltzmann and consider entropy as a measure
for thermodynamic probability, then when a physical
state such as a volume of gas, with various degrees of
freedom and endowed with a definite energy, has
reached a condition of thermodynamic equilibrium, the
entropy in such a case will be nothing more than
the number of the multiform states which such a system
can assume under given conditions. And if the entropy
thus considered possesses an absolute value this means
that the number of possible states under the given con-
ditions is quite definite and finite.

At the time of Clausius and Helmholtz and Boltz-
mann such an assertion would have been considered
entirely out of the question. The differential equations
of classical dynamics were then looked upon as the sole

192 WHERE IS SCIENCE GOING?

fundamentals of physical science. Therefore it was
necessary to consider physical states as continuous, and
all possibilities of change as infinite in their measurable
quantities. Since the introduction of the quantum hy-
pothesis the state of affairs is different, and I feel that
we have not long to wait before it will be possible to speak
in quite a different way of a definite number of possible
states and of absolute measures of entropy correspond-
ing to them, without thereby running up too violently
against the accepted physical notions of the time. Indeed
the new quantum axiom has already produced results
that can favorably compare with the most fruitful
theories of the past. In the case of radiant heat it has
led to the formulation of laws of energy which explain
the normal spectrum. In the laws of thermodynamics
it has found its expression in the theory established
by W. Nernst, which has been corroborated on many
sides 5 and the basis of the quantum hypothesis has been
so far expanded that from it we can deduce not only
the existence but also the numerical values of the so-
called chemical constants. In regard to the constitution
of the atom the ideas of Niels Bohr have been the
starting-point for the establishment of the so-called
stationary electronic orbits, and thus the ground was
prepared for solving the riddle of the spectroscopic
phenomena. Indeed, unless all signs be misleading, a
process seems to be developing which may be called
the reduction of all physical theories to arithmetical
terms, because a large number of physical dimensions
which hitherto had been looked upon as continuous

FROM RELATIVE TO ABSOLUTE 193

have been shown under the microscopic examination of
a sharper analysis to be discontinuous and numerable.
Along these lines the measurements which have been
arrived at by L. S. Ornstein, the head of the Physical
Institute at Utrecht, are indicative. These measurements
show that the ratio of intensity of the components of
spectral multiplets can be given in simple integral num-
bers. And Max Born's interesting attempt to supplant
the differential calculus of physical mechanics by equa-
tions of finite differences points in the same direction.

The outstanding cases that I have here chosen point
to a definite Drang or fundamental urge which seems to
characterize the advance of physical science. In these
cases the movement has undoubtedly been from the
relative to the absolute. Now comes the question: How
far can we say that this advance is definitely character-
istic of the progress of physical science as a whole? It
would be saying too much, perhaps, if I were to answer
the question by an unqualified affirmative. Indeed I can
easily imagine that some of my readers may be of the
opposite view, and may already be thinking in their own
minds that this chapter could be written in the reverse
direction and called "From the Absolute to the Rela-
tive." They certainly would find material at hand which
at least on the surface offers tempting ground to stand
upon. It might, for instance, be urged that the concept
of atomic weight could be taken as pointing in a direc-
tion contrary to that which I have suggested. My im-
aginary opponent might say that the numeral which I
have indicated as representing the absolute weight of an

194 WHERE IS SCIENCE GOING?

atom is by no means absolute. In view of the fact that
an element generally possesses several isotopes with a
different atomic weight, the measured atomic weight
presents a more or less contingent addition which is a
sort of average value, that is quite dependent on the
ratio of the various isotopes in the compound under
analysis. Even if we were to take only one single isotope
into consideration, from the standpoint of our present
knowledge it would be quite unscientific to consider
this as something absolute. The most modern opinion,
which is backed up by the Rutherford experiment of
bombarding the nucleus of the atom, would seem to
be in the direction of reviving Prout's hypothesis and
referring the constitution of all chemical elements to
the basic atom of hydrogen. Therewith the concept of
atomic weight would fundamentally be a relative num-
ber. Having thus gained what at least appears to be a
signal victory in this one instance, my opponent might
play his trump card and throw the Einstein General
Theory of Relativity on the table. He might very well
urge that to talk of the concepts of space and time as
something absolute belongs to the past and signifies
retrogression rather than progress. In other words, one
of the most signal advances in modern physics is
stamped with the idea of the relative rather than the
absolute.

The first and most obvious reply to such a criticism
is to call attention to the danger of applying scientific
terms to facts and meanings for which they were never
intended. I have already shown how the theory of

FROM RELATIVE TO ABSOLUTE 195

relativity has actually led to the discovery of an absolute
measure by which the energy of a body at rest
may be formulated. Therefore it is clear that the term,
Relativity , does not refer to physics as a whole and
must not be taken out of its special scientific context.
It would be quite superficial to take the relativity of
time and space, and halt firmly within the confines of
that concept without asking whither it leads. As a matter
of fact the concept of relativity is based on a more
fundamental absolute than the erroneously assumed
absolute which it has supplanted. Over and over again
in the history of science it has happened that concepts
which at one time were looked upon as absolute were
subsequently shown to be only of relative value j and
this is exactly what has happened in regard to the
former concept of space and time. But when an absolute
concept is thus relativized, this does not mean that the
quest of the absolute becomes eliminated from scientific
progress. It rather means that a more fundamental con-
cept takes its place and a more fundamental advance is
thus achieved. If we admit the concept of relativity at
all we must admit the acceptance of an absolute, because
it is out of this that the relative concept as such arises.
Supposing, for instance, a scientific researcher worked
for years and years on the problem of discovering the
cause of some special event in nature and found all his
efforts baffled, would he thereby be justified in declaring
that the event has no cause at all? The fact is that we
cannot relativize everything any more than we can de-
fine and explain everything. There are fundamentals

196 WHERE IS SCIENCE GOING?

that cannot be defined or explained, because they form
the bedrock of all our knowledge. Every definition must
necessarily rest on some concept which does not call for
definition at all. And it is the same with every form of
proof. We cannot define a thing except in terms that are
already known and accepted, and we cannot prove any-
thing except from something that is already admitted.
If we wish to establish a truth by the inductive method
it must be on the basis of accepted facts. And if we
wish to establish a truth by the process of deductive
reasoning the principle from which the deduction pro-
ceeds must be accepted as absolute. Therefore the
relativist concept must necessarily have the concept of
the absolute as its foundation. If we once remove the
absolute, then the whole relativist theory will fall to the
ground, just as an overcoat would fall if the peg on
which it hangs should disappear. These considerations
are quite sufficient, I think, to suggest the reply which
might be given to the counter argument of my im-
aginary disputant.

If eventually it should turn out possible to refer the
atomic weights of all elements to the atomic weight of
hydrogen, then we should have achieved one of the
most fundamental results in the history of the scientific
investigation of matter. The significance of it would
be that in the light of this explanation matter could
be proved to have one simple origin. Then the two
factors of the hydrogen atom, namely, the positively
charged hydrogen nucleus (the so-called proton) and
the negatively charged electron, together with the ele-

FROM RELATIVE TO ABSOLUTE 197

mental quantum of action, would represent the founda-
tion-stones on which the structure of the physical world
is built. Now these quantities should be considered as
absolute as long as they do not depend upon one another
or something outside of them. There we should have
the absolute once again, only at a higher level and in a
simpler form. If we like to unroll the thread of this
thought a little further, we might ask, what is the
foundation on which the great relativist theory is built?
Einstein explained that our concepts of space and time,
which were recognized by Newton and Kant as absolute
forms of all knowledge, really possessed only a relative
significance, inasmuch as they depended on an arbitrary
selection of the reference system and the means of
measurement. It is a familiar fact that we cannot ob-
serve the motion of any body without reference to some
other body. It was to meet this difficulty that Newton
adopted the hypothesis of absolute space. The "fixed"
stars were used to define absolute space. The stars,
however, are not fixed even relatively to one another.
Therefore the concept of absolute space and the refer-
ence points according to which it was "fixed" were quite
arbitrary. This explanation goes perhaps to the deepest
root of our scientific thought. If from space and time we
should take away the concept of the absolute, this does
not mean that the absolute is thereby banished out of
existence, but rather that it is referred back to something
more fundamental. As a matter of fact, this more
fundamental thing is the four-dimensional manifold
which is constituted by the welding together of time

198 WHERE IS SCIENCE GOING?

and space into a single continuum. Here the standard
of reference and measurement is independent of
arbitrary choice and is absolute.

It only takes a little reflection to realize the fact that
the much misunderstood relativity theory by no means
gets rid of the absolute but, on the contrary, that it has
brought out the absolute into sharper definition, inas-
much as it points out how, and how far, physical science
is based on the existence of an absolute in the outer
world. If we should say, as several epistemologists do,
that the absolute is to be found only in the individual's
sensory data of perception, then there ought to be as
many kinds of physical science as there are physicists,
and we should be utterly unable to explain how it is
that up to now each discoverer in physical science has
been standing on the shoulders of his predecessors, as it
were, and has taken their findings as the basis of his
work. Indeed it is exclusively on the basis of cooperative
labor and the acceptance by others of the findings of the
various individual researchers, that we can explain the
structure of physical science as we have it to-day. That
we do not construct the external world to suit our own
ends in the pursuit of science, but that vice versa the
external world forces itself upon our recognition with
its own elemental power, is a point which ought to be
categorically asserted again and again in these positivistic
times. From the fact that in studying the happenings of
nature we strive to eliminate the contingent and acci-
dental and to come finally to what is essential and
necessary, it is clear that we always look for the basic

FROM RELATIVE TO ABSOLUTE 199

thing behind the dependent thing, for what is absolute
behind what is relative, for the reality behind the
appearance and for what abides behind what is transi-
tory. In my opinion, this is characteristic not only of
physical science but of all science. Further, it is not
merely a characteristic of all kinds of human endeavor
to attain to the knowledge of any subject, but it is also
characteristic of those branches of human effort that
strive to formulate ideas of the good and the beautiful.

Here I am going wide of my purpose ; for the plan
I had in mind at the beginning of this essay was not
to make assertions and then prove them, but rather
to call attention to certain actual changes which have
taken place in the course of scientific development and
allow the bare presentation of facts to leave its own
impression on the mind of the reader.

Before closing I should like to raise the most difficult
question of all. It is this: How can we say that a scientific
concept, to which we now ascribe an absolute character,
may not at some future date show itself to have only a
certain relative significance and to point to a further
absolute? To that question only one answer can be given.
After all I have said, and in view of the experiences
through which scientific progress has passed, we must
admit that in no case can we rest assured that what is
absolute in science to-day will remain absolute for all
time. Not only that, but we must admit as certain the
truth that the absolute can never finally be grasped by
the researcher. The absolute represents an ideal goal
which is always ahead of us and which we can never

200 WHERE IS SCIENCE GOING?

reach. This may be a depressing thought -y but we must
bear with it. We are in a position similar to that of a
mountaineer who is wandering over uncharted spaces,
and never knows whether behind the peak which he sees
in front of him and which he tries to scale there may
not be another peak still beyond and higher up. Yet
it is the same with us as it is with him. The value of the
journey is not in the journey's end but in the journey
itself. That is to say, in the striving to reach the goal
that we are always yearning for, and drawing courage
from the fact that we are always coming nearer to it.
To bring the approach closer and closer to truth is the
aim and effort of all science.

Here we can apply the saying of Gotthold Ephraim
Lessing: "Not the possession of truth but the effort in
struggling to attain to it brings joy to the researcher."
We cannot rest and sit down lest we rust and decay.
Health is maintained only through work. And as it
is with all life so it is with science. We are always
struggling from the relative to the absolute.

EPILOGUE
A SOCRATIC DIALOGUE

Interlocutors: PLANCK EINSTEIN MURPHY

Note: — The following is an abridgment of stenographic re forts
made by an attendant secretary during various conversations

murphy: I have been collaborating with our friend,
Planck, on a book which deals principally with the
problem of causation and the freedom of the
human will.

einstein: Honestly I cannot understand what people
mean when they talk about the freedom of the
human will. I have a feeling, for instance, that
I will something or other ; but what relation this
has with freedom I cannot understand at all. I
feel that I will to light my pipe and I do it; but
how can I connect this up with the idea of free-
dom? What is behind the act of willing to light
the pipe? Another act of willing? Schopenhauer
once said: Der Mensch kann was er will; er kann
aber nicht wollen was er will (Man can do what he
wills but he cannot will what he wills).

murphy: But it is now the fashion in physical science
to attribute something like free will even to the
routine processes of inorganic nature.

einstein: That nonsense is not merely nonsense. It is
objectionable nonsense.

201

202 WHERE IS SCIENCE GOING?

murphy: Well, of course, the scientists give it the name
of indeterminism.

einstein: Look here. Indeterminism is quite an illogical
concept. What do they mean by indeterminism?
Now if I say that the average life-span of a radio-
active atom is such and such, that is a statement
which expresses a certain order, Gesetzlichkeit, But
this idea does not of itself involve the idea of
causation. We call it the law of averages j but not
every such law need have a causal significance. At
the same time if I say that the average life-span
of such an atom is indetermined in the sense of
being not caused, then I am talking nonsense. I
can say that I shall meet you to-morrow at some
indetermined time. But this does not mean that
time is not determined. Whether I come or not
the time will come. Here there is question of
confounding the subjective with the objective
world. The indeterminism which belongs to quan-
tum physics is a subjective indeterminism. It must
be related to something, else indeterminism has no
meaning, and here it is related to our own inability
to follow the course of individual atoms and fore-
cast their activities. To say that the arrival of a
train in Berlin is indetermined is to talk nonsense
unless you say in regard to what it is indetermined.
If it arrives at all it is determined by something.
And the same is true of the course of atoms. ,

murphy: In what sense then do you apply determinism
to nature? In the sense that every event in nature

EPILOGUE 203

proceeds from another event which we call the
cause?

Einstein: I should hardly put it that way. In the first
place, I think that much of the misunderstanding
encountered in all this question of causation is due
to the rather rudimentary formulation of the
causal principle which has been in vogue until
now. When Aristotle and the scholastics defined
what they meant by a cause, the idea of objective
experiment in the scientific sense had not yet
arisen. Therefore they were content with defining
the metaphysical concept of cause. And the same
is true of Kant. Newton himself seems to have
realized that this pre-scientific formulation of the
causal principle would prove insufficient for
modern physics. And Newton was content to
describe the regular order in which events happen
in nature and to construct his synthesis on the
basis of mathematical laws. Now I believe that
events in nature are controlled by a much stricter
and more closely binding law than we suspect
to-day, when we speak of one event being the
cause of another. Our concept here is confined to
one happening within one time-section. It is
dissected from the whole process. Our present
rough way of applying the causal principle is
quite superficial. We are like a child who judges
a poem by the rhyme and knows nothing of the
rhythmic pattern. Or we are like a juvenile
learner at the piano, just relating one note to that

204 WHERE IS SCIENCE GOING?

which immediately precedes or follows. To an
extent this may be very well when one is dealing
with very simple and primitive compositions j but
it will not do for the interpretation of a Bach
Fugue. Quantum physics has presented us with
very complex processes and to meet them we
must further enlarge and refine our concept of
causality.

murphy: You'll have a hard job of it, because you'll
be going out of fashion. If you will permit me to
make a little speech I shall do so, not so much
because I like to listen to my own talk, though
of course I do — what Irishman doesn't? — but
rather because I should like to have your reactions
to it.

Einstein: Gewiss.

murphy: The Greeks made the workings of fate or
destiny the basis of their drama ; and drama in
those days was a liturgical expression of the pro-
found irrationally perceiving consciousness. It was
not merely a discussion, like a Shavian play. You
remember the tragedy of Atreus, where fate, or
the ineluctable sequence of cause and effect, is the
sole simple thread on which the drama hangs.

einstein: Fate, or destiny, and the principle of causa-
tion are not the same thing.

murphy: I know that. But scientists live in the world
just like other people. Some of them go to political
meetings and the theater and mostly all that I
know, at least here in Germany, are readers of

EPILOGUE 205

current literature. They cannot escape the influ-
ence of the milieu in which they live. And that
milieu at the present time is characterized largely
by a struggle to get rid of the causal chain in
which the world has entangled itself.

einstein: But isn't mankind always struggling to get
rid of that causal chain?

murphy: Yes, but that is not to the point just at the
moment. Anyhow I doubt if the politician ever
contemplates the consequences of the causal se-
quence he sets afoot by his foolishness. He is too
nimble himself and can slip out through the links.
Macbeth was not a politician. And that is where
he failed. He realized that the assassination could
not trammel up the consequence. But he did not
think of how to escape from the sequential shackles
until it was too late. And this is because he was
not a politician. My point here is that there is a
universal recognition at the moment of this in-
exorable sequence. People are realizing what Ber-
nard Shaw told them long ago — which of course
had been told on innumerable occasions previously
— when he wrote Caesar and Cleofatra. You re-
member Caesar's speech to the Queen of Egypt
after her orders to slay Photinus had been carried
out, though Caesar had guaranteed his safety.

"Do you hear?" says Caesar. "Those knockers
at your gate are also believers in vengeance and
in stabbing. You have slain their leader j it is
right that they shall slay you. If you doubt it, ask

206 WHERE IS SCIENCE GOING?

your four councillors here. And then in the name
of right shall I not slay them for murdering their
Queen, and be slain in my turn by their country-
men as the invader of their Fatherland? Can Rome
do less than slay these slayers too, to show the
world how Rome avenges her sons and her honor?
And so, to the end of history, murder shall breed
murder, always in the name of right and honor
and peace, until the gods are tired of blood and
[create a race that shall understand."

People realize this terrible truth nowadays, not
indeed because they see that blood will have blood
but because they see that in robbing your neighbor
you rob yourself ; for robbery will have robbery
just as blood will have blood. The so-called victors
in the world war robbed the vanquished and they
now know that in doing so they robbed themselves.
So now we have a condition of all-round misery.
People at large see that 5 but they haven't the
courage to face it and they race, like Macbeth, to
the witches' cauldron. In this case unfortunately
science is one of the ingredients thrown into the
cauldron to give them the solvent they are looking
for. Instead of boldly admitting the mess, the
tragedy, the crime, everybody wants to try to prove
himself innocent, and looks for the proof by try-
ing to find an alibi for the consequences of his
own deeds. Look at that string of hungry people
coming to your door every day for bread. Able-
bodied fellows who want to exercise man's privi-

EPILOGUE 207

lege, which is to work. You have them also
parading the streets of London, with their Dis-
tinguished Conduct Medals on their breasts,
shouting for bread. And you have the same in
New York and Chicago and Rome and Turin.
The comfortable person who sits in his easy chair
says to himself "This has nothing to do with us."
And he says that because he knows it has. Then he
takes up his popular writers of physics and gives
a sigh of contentment when he is told that nature
knows no such thing as the law of consequences.
What more do you want? Here is Science? and
Science is the modern counterpart of religion. It is
your comfortable bourgeois who has endowed
scientific institutions and laboratories. And, say
what you will, scientists would not be human if
they did not, at least unconsciously, share in the
same spirit.

Einstein: Ach das kann man nicht sagen.

murphy: Yes. That can man very well say. You re-
member your own picture of the self-seekers in
the temple of science, whom you admit have built
even a great portion of the structure, while you
acknowledge that only a few have found favor
with the angel of God. I am inclined to think that
the struggle of science at the present moment is
the effort to keep its thought-scheme clear of the
confusion which the popular spirit would bring
into it. It is much the same struggle as the old
theologians had. At the Renaissance, however, they

WHERE IS SCIENCE GOING?

succumbed to the fashion of the time and intro-
duced foreign ideas and methods into their science,
which finally resulted in the scholastic break-up.

The decline of scholasticism dates from the
time when the mob started running after the
philosophers and theologians. Remember how they
rushed helter-skelter to hear Abelard in Paris,
though it is obvious that they could not understand
his distinctions. Public flattery was more the cause
of his downfall than any merely private influences.
He would not have been human if he had not been
tempted to think himself above his science, and he
succumbed to the temptation. I am not so sure that
many scientists are not in his place to-day. Some
of the glistening webs of fancy that they weave
seem very much akin to the sophistic distinctions
of the scholastic decadence.

The older philosophers and theologians were
aware of this danger and they contrived to offset
it. They had their esoteric bodies of doctrine
which were disclosed only to the initiated. We
have the same sort of protection evidenced in
other branches of culture to-day. The Catholic
Church has widely maintained its ritual and
dogmas within the forms and formulations of a
language which the populace does not understand.
The sociologists and financial experts have a
jargon that is all their own and it saves them
from being found out. The majesty of the law is
upheld in like manner and the medical craft could

EPILOGUE 209

not survive if it prescribed its medicines and de-
scribed its diseases in the vernacular. But all these
do not matter because none of all these sciences
or arts or crafts is vital. Physical science is or-
ganically vital at the moment and for that reason
it seems to be suffering from

einstein: But I can think of nothing more objection-
able than the idea of science for the scientists.
It is almost as bad as art for the artists and
religion for the priests. There is certainly some-
thing in what you say. And I believe that the
present fashion of applying the axioms of physical
science to human life is not only entirely a mis-
take but has also something reprehensible in it.
I find that the problem of causality which is
to-day under discussion in physics is not a new
phenomenon in the field of science. The method
which is being used in quantum physics has
already had to be applied in biology, because the
biological processes in nature could not in them-
selves be traced so that their connection would
be clear, and for that reason biological rules have
always been of a statistical character. And I do
not understand why so much pother ought to be
made if the principle of causation should undergo
a restriction in modern physics, for this is not a
new situation at all.

murphy: Of course it has not brought about any new
situation 5 but biological science is not vital in the
way that physical science is vital at the moment.

2io WHERE IS SCIENCE GOING?

People are no longer very much interested whether
we were descended from monkeys or not, except
certain animal enthusiasts who think the idea rather
rough on the monkey. And there is not that public
interest in biology such as there was in the time of
Darwin and Huxley. The center of gravity of the
public interest has shifted to physics. That is why
the public reacts in its own way to any new for-
mulation in physics.

Einstein: I am entirely in agreement with our friend
Planck in regard to the stand which he has taken
on this principle, but you must remember what
Planck has said and written. He admits the im-
possibility of applying the causal principle to the
inner processes of atomic physics under the present
state of affairs; but he has set himself definitely
against the thesis that from this Unbrauchbarkeit
or inapplicability we are to conclude that the
process of causation does not exist in external
reality. Planck has really not taken up any definite
standpoint here. He has only contradicted the em-
phatic assertions of some quantum theorists and I
agree fully with him. And when you mention
people who speak of such a thing as free will in
nature it is difficult for me to find a suitable reply.
The idea is of course preposterous.

murphy: You would agree then, I imagine, that physics
gives no ground whatsoever for this extraordinary
application of what we may for convenience's sake
call Heisenberg^ principle of indeterminacy.

EPILOGUE

211

einstein: Of course I agree.

murphy: But then you know that certain English phy-
sicists of very high standing indeed and at the
same time very popular have promulgated with
emphasis what you and Planck call, and many
others with you, unwarranted conclusions.

einstein: You must distinguish between the physicist
and the litterateur when both professions are com-
bined into one. In England you have a great
English literature and a great discipline of style.
What I mean is that there are scientific writers in
England who are illogical and romantic in their
popular books, but in their scientific work they are
acute logical reasoners.

What the scientist aims at is to secure a logically
consistent transcript of nature. Logic is for him
what the laws of proportion and perspective are to
the painter, and I believe with Henri Poincare
that science is worth pursuing because it reveals the
beauty of nature. And here I will say that the
scientist finds his reward in what Henri Poincare
calls the joy of comprehension, and not in the
possibilities of application to which any discovery
of his may lead. The scientist, I think, is content
to construct a perfectly harmonious picture on a
mathematical pattern, and he is quite satisfied to
connect up the various parts of it through mathe-
matical formulas without asking whether and how
far these are a proof that the law of causation
functions in the external world.

2i2 WHERE IS SCIENCE GOING?

murphy: Let me call your attention, Professor, to a
phenomenon that happens sometimes down there
on the lake when you are sailing your yacht. Of
course it doesn't happen very often on the placid
waters of Caputh, because you have flat lands
all around and therefore no sudden wind squalls.
But if you are sailing close to the wind on one of
our northern lakes, you are always running the
risk of keeling over rather suddenly under the
onslaught of an unexpected air current. What I
am coming to is, that I think the positivist might
easily get in his shot here and hit you between
wind and water. If you say that the scientist is
content to secure mathematical logic in his mental
construct, then you will quickly be quoted in sup-
port of the subjective idealism championed by
modern scientists such as Sir Arthur Eddington.

einstein: But that would be ridiculous.

murphy: Of course it would be an unjustifiable conclu-
sion j but you have already been widely quoted in
the British Press as subscribing to the theory that
the outer world is a derivative of consciousness.
I have had to call this to the attention of a friend
of mine in England, Mr. Joad, who has written
an excellent book called Philosophical Aspects of
Science. The book is a contradiction of the attitudes
taken up by Sir Arthur Eddington and Sir James
Jeans and your name is mentioned as corroborating
their theories.

EPILOGUE 213

einstein: No physicist believes that. Otherwise he
wouldn't be a physicist. Neither do the physicists
you have mentioned. You must distinguish be-
tween what is a literary fashion and what is a
scientific pronouncement. These men are genuine
scientists and their literary formulations must not
be taken as expressive of their scientific convictions.
Why should anybody go to the trouble of gazing
at the stars if he did not believe that the stars were
really there? Here I am entirely at one with
Planck. We cannot logically prove the existence
of the external world, any more than you can
logically prove that I am talking with you now or
that I am here. But you know that I am here and
no subjective idealist can persuade you to the
contrary.

murphy: That point, of course, was fully elucidated
long ago by the scholastics, and I cannot help
thinking that much of the confusion in the nine-
teenth century and to-day would have been spared
if the break with the philosophical tradition had
not been so abysmal in the seventeenth century.
The scholastics put the case for the modern
physicist very clearly in describing mental images
of external reality as existing fundamentaliter in rey \\
formaliter in mente.

I forget how the discussion on this particular topic broke
off. In the stenogram the next paragraph opens with
Planck. There has recently been a great deal of dis-

214 WHERE IS SCIENCE GOING?

cussion in the Press, I said to him, about what is called
the bankruptcy of science. Is it that the general public
here feels, somehow or other, that all the great scientific
achievements of Germany seem to have been of no
avail in securing the prestige of the nation abroad? Of
course there is the larger background also of the general
skepticism which is a universal feature of the world in
our day. This attacks religion and art and literature
as well as science.

planck : The churches appear to be unable to supply
that spiritual anchorage which so many people are
seeking. And so the people turn in other directions.
The difficulty which organized religion finds in
appealing to the people nowadays is that its appeal
necessarily demands the believing spirit, or what is
generally called Faith. In an all-round state of
skepticism this appeal receives only a poor re-
sponse. Hence you have a number of prophets
offering substitute wares.

murphy: Do you think that science in this particular
might be a substitute for religion?

planck: Not to a skeptical state of mindj for science
demands also the believing spirit. Anybody who
has been seriously engaged in scientific work of any
kind realizes that over the entrance to the gates
of the temple of science are written the words:
Ye must have faith. It is a quality which the
scientists cannot dispense with.

The man who handles a bulk of results obtained

EPILOGUE 215

from an experimental process must have an im-
aginative picture of the law that he is pursuing.
He must embody this in an imaginary hypothesis.
The reasoning faculties alone will not help him
forward a step, for no order can emerge from that
chaos of elements unless there is the constructive
quality of mind which builds up the order by a
process of elimination and choice. Again and again
the imaginary plan on which one attempts to build
up that order breaks down and then we must try
another. This imaginative vision and faith in the
ultimate success are indispensable. The pure
rationalist has no place here.

murphy: How far has this been verified in the lives
of great scientists? Take the case of Kepler, whose
300th anniversary we were celebrating, you re-
member, that evening when Einstein gave his
lecture at the Academy of Science. Wasn't there
something about Kepler having made certain dis-
coveries, not because he set out after them with
his constructive imagination, but rather because he
was concerned about the dimensions of wine barrels
and was wondering which shapes would be the
most economic containers?

planck : These stories circulate in regard to nearly
everybody whose name is before the public. As a
matter of fact, Kepler is a magnificent example of
what I have been saying. He was always hard up.
He had to suffer disillusion after disillusion and
even had to beg for the payment of the arrears of

2i6 WHERE IS SCIENCE GOING?

his salary by the Reichstag in Regensburg. He had
to undergo the agony of having to defend his own
mother against a public indictment of witchcraft.
But one can realize, in studying his life, that what
rendered him so energetic and tireless and pro-
ductive was the profound faith he had in his own
science, not the belief that he could eventually
arrive at an arithmetical synthesis of his astro-
nomical observations, but rather the profound faith
in the existence of a definite plan behind the whole
of creation. It was because he believed in that plan
that his labor was felt by him to be worth while
and also in this way, by never allowing his faith
to flag, his work enlivened and enlightened his
dreary life. Compare him with Tycho de Brahe.
Brahe had the same material under his hands as
Kepler, and even better opportunities, but he re-
mained only a researcher, because he did not have
the same faith in the existence of the eternal laws
of creation. Brahe remained only a researcher , but
Kepler was the creator of the new astronomy.

Another name that occurs to me in this connec-
tion is that of Julius Robert Mayer. His discoveries
were hardly noticed, because in the middle of last
century there was a great deal of skepticism, even
among educated people, about the theories of
natural philosophy. Mayer kept on and on, not
because of what he had discovered and could prove,
but because of what he believed. It was only in
1869 tnat tne Society of German Physicists and

EPILOGUE 217

Physicians, with Helmholtz at their head, recog-
nized Mayer's work.

murphy: You have often said that the progress of
science consists in the discovery of a new mystery
the moment one thinks that something funda-
mental has been solved. The quantum theory has
opened up this big problem of causation. And I
really do not think that the matter can be answered
very categorically. Of course it is easy enough to
see that those who take up a definite stand and say
that there is no such thing as causality are illogical,
in the sense that you cannot prove any such state-
ment either by experiment or by appeal to the
direct dictates of consciousness and common sense
in its defense. But, all the same, it seems to me
that the burden is on the determinists at least to
indicate the direction in which the old formulation
of causality will have to be revised in order to
meet the needs of modern science.

planck : As to the first point, that about the discovery
of new mysteries. This is undoubtedly true. Science
cannot solve the ultimate mystery of nature. And
that is because, in the last analysis, we ourselves
are part of nature and therefore part of the mys-
tery that we are trying to solve. Music and art are,
to an extent, also attempts to solve or at least to
express the mystery. But to my mind the more
we progress with either the more we are brought
into harmony with all nature itself. And that is one
of the great services of science to the individual.

2i8 WHERE IS SCIENCE GOING?

murphy: Goethe once said that the highest achieve-
ment to which the human mind can attain is an at-
titude of wonder before the elemental phenomena
of nature.

planck : Yes, we are always being brought face to face
with the irrational. Else we couldn't have faith.
And if we did not have faith but could solve every
puzzle in life by an application of the human
reason, what an unbearable burden life would be.
We should have no art and no music and no
wonderment. And we should have no science ; not
only because science would thereby lose its chief
attraction for its own followers — namely, the pur-
suit of the unknowable — but also because science
would lose the cornerstone of its own structure,
which is the direct perception by consciousness of
the existence of external reality. As Einstein has
said, you could not be a scientist if you did not
know that the external world existed in reality j
I but that knowledge is not gained by any process of
reasoning. It is a direct perception and therefore
in its nature akin to what we call Faith. It is a
metaphysical belief. Now that is something which
the skeptic questions in regard to religion ; but it is
the same in regard to science. However, there is
this to be said in favor of theoretical physics, that
it is a very active science and does make an appeal
to the lay imagination. In that way it may, to some
extent, satisfy the metaphysical hunger which
religion does not seem capable of satisfying

EPILOGUE 219

nowadays. But this would be entirely by stimulat-
ing the religious reaction indirectly. Science as such
can never really take the place of religion. This
is explained in the penultimate chapter of the book.

murphy: And now for the second part of the question,
that of the direction in which the traditional for-
mulation of the causality principle may be revised.
Einstein talks about the development of our facul-
ties of perception as science goes on.

planck : What exactly does he mean?

murphy: Perhaps I had better put it in my own way.
Take for instance the modern phenomenon of
speed. Fifty years ago the average tempo of
locomotion was that of a trotting horse. Now it
is even more than that of the railway train. If we
strike a mean between the railway train and the
motor car and the aeroplane, we had better say
sixty miles an hour instead of six miles an hour,
as in the days of horse locomotion. You remember
when bicycles first became popular. People were
running down children and women on the roads
day after day. Now you could not run down your
grandmother with a bicycle. She'd be out of the
way too quickly. You remember that when motors
first careered along the roads the horses took
fright. Now even the horses have developed their
faculties to harmonize their perceptions with the
idea of the new speed. There can be no doubt but
that modern mankind has developed some faculty
or other in regard to this new phenomenon of

WHERE IS SCIENCE GOING?

speed. Now I think Einstein's idea is that this sort
of thing will go on developing, and that scientists
will arise who will have a much keener perception
than the scientists of to-day. They will, of course,
also have more delicate instruments. But the point
is that what we need to develop are the perceptive
faculties themselves. It may be that a race of
scientists trained in the laboratory will be able
eventually to perceive the profound and manifold
operation of causation in nature, just as the great
musical genius perceives inner harmonies which the
philistine cannot even dream of, and just as the
music-lover can perceive keenly the beauty of a
Beethoven symphonic structure, which the peasant
could not appreciate at all, because he is accustomed
only to his simple folk melodies. The development
of the powers of perception therefore is one of the
main tasks we have to meet. That seems to be
Einstein's idea.

tck: Of course it is clear. There is no doubt what-
soever that the stage at which theoretical physics
has now arrived is beyond the average human
faculties, even beyond the faculties of the great
discoverers themselves. What, however, you must
remember is that even if we progressed rapidly in
the development of our powers of perception we
could not finally unravel nature's mystery. We
could see the operation of causation, perhaps, in
the finer activities of the atoms, just as on the
old basis of the causal formulation in classical

EPILOGUE

221

mechanics we could perceive and make material
images of all that was observed as occurring in
nature.

Where the discrepancy comes in to-day is not
between nature and the principle of causality, but
rather between the picture which we have made of
nature and the realities in nature itself. Our picture
is not in perfect accord with our observational re-
sults -j and, as I have pointed out over and over
again, it is the advancing business of science to
bring about a finer accord here. I am convinced that
the bringing about of that accord must take place,
not in the rejection of causality, but in a greater
enlargement of the formula and a refinement of
it, so as to meet modern discoveries.

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